The first two terms in an arthemetic progression are 2 and 9. The last term in the progression is the only number greater than 150. Find the sum of all the terms in the progression

Answer:

(a) G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84

(b) A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 -     1900^2) - 0.10(t - 1900)

Step-by-step explanation:

(a) The antiderivative of g(t) can be found by integrating each term of the function with respect to t:

∫g(t) dt = ∫(1.68 × 10^-4)t^2 dt - ∫0.02t dt - ∫0.10 dt

= (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t + C

where C is the constant of integration.

To find the specific antiderivative G(t) that passes through the point (1970, 94.8), we can use this point to solve for C:

94.8 = (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970) + C

C = 94.8 + (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970)

C ≈ -2445.84

Therefore, the specific antiderivative that gives the gender ratio is:

G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84

(b) The accumulation function of g is the integral of g with respect to t, or:

A(t) = ∫g(t) dt = G(t) + C

where C is the constant of integration. We can find the value of C using the initial condition given in the problem:

A(1900) = ∫g(t) dt ∣t=1900 = G(1900) + C = 0

Therefore, C = -G(1900), and the accumulation function of g is:

A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 - 1900^2) - 0.10(t - 1900)

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The project completion time is output of the simulations, option A, the EXCEL function used is (c) 1+4*RAND() and the standard deviation is

(b) 1.47.

1) In this simulation, we enter commands based on the way that activity durations are distributed (here uniformly with predetermined intervals). We determine the project completion time as an output based on the command we used and our calculations. This value will fluctuate (slightly) when the simulation is run, hence it is not fixed.

Hence, the "project completion time" is an (a) Output of the simulation.

2) Here, it is given that time required to complete activity A is uniformly distributed in an interval [1, 5].

So, we require random numbers starting from 1 with an interval of length 5-1=4.

We know, during simulation using usual Excel function RAND() we obtain random numbers in an interval [0, 1].

Thus if we multiply usual Excel function RAND() by 4 and thus use 4*RAND(), then we obtain random numbers in an interval [0*4, 1*4] i.e

[0, 4].

Adding 1 to this Excel function i.e. using Excel function 1+4*RAND() we obtain random numbers in an interval [0+1, 4+1] i.e [1, 5].

Hence, the Excel function to be used to generate random numbers for the duration of activity A is (c) 1+4*RAND().

3) For [tex]\tiny X\sim Unif\left ( a,b \right )[/tex], variance is given by

[tex]\tiny Var\left ( X \right )=\frac{\left ( b-a \right )^2}{12}[/tex]

Variance for activity A is given by

[tex]\tiny \frac{\left ( 5-1 \right )^2}{12}=\frac{4^2}{12}=1.333333[/tex]

Variance for activity B is given by

[tex]\tiny \frac{\left ( 3-2 \right )^2}{12}=\frac{1^2}{12}=0.083333[/tex]

Variance for activity C is given by

[tex]\tiny \frac{\left ( 6-3 \right )^2}{12}=\frac{3^2}{12}=0.75[/tex]

Variance of project completion time in the project is \tiny [tex]1.333333+0.083333+0.75= 2.166666[/tex]

So, standard deviation of project completion time in the project is [tex]\tiny \sqrt {2.166666}=1.47196\approx 1.47[/tex]

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Complete question:

A project has three activities A, B, and C that must be carried out sequentially. The probability distributions of the times required to complete each of the activities A, B, and C are uniformly distributed in intervals (1,5), (2,3) and (3,6) respectively. Find the total project completion time and run 1000 simulation trials in Excel. 7. The "project completion time" is a(n)... a. Output of the simulation b. Input of the simulation c. Decision variable in the simulation d. A fixed value in the simulation 8. Which of the following Excel functions would properly generate a random number for the duration of activity A in the project described above? a. 5* RANDO b. 1+5 * RANDO c. 1+4* RANDO d. NORM.INV(RAND(),1,5) e. NORM.INV(RAND(0,5,1) 9. The standard deviation of the project completion time in the project described above is cl a 2.83 b. 1.47 c. 1.15 d. 1.82 e. 1.63

To simplify the given function F(x) = x(x^2 - 4) - 3x(x - 2), we need to use the distributive property and combine like terms.

First, we distribute x in the first term, and we get:

F(x) = x^3 - 4x - 3x^2 + 6x

Next, we can combine like terms:

F(x) = x^3 - 3x^2 + 2x

Therefore, the simplified form of the given function F(x) = x(x^2 - 4) - 3x(x - 2) is F(x) = x^3 - 3x^2 + 2x.

Answer:

Begin by simplifying the phrases within the brackets, beginning with the innermost brackets:

(2 x 3)^-1 = 1/6 (because 2 x 3 = 6, and the negative exponent flips the fraction)

1/2^3 = 1/8 (because 2^3 = 8)

So, (2x3)^-1x1/2^3 = 1/6 x 1/8 = 1/48

Next, simplify the expression outside the parentheses:

(3x2^2)^-2 = 1/(3x2^2)^2 = 1/(3^2 x 2^4) = 1/36 x 1/16 = 1/576

Now, substitute the simplified terms back into the original expression and simplify:

3x(1/48)x(1/576) = 1/768

So the final answer is 1/768.

The mass of the cylinder of lead with a radius of 1 centimeter and a height of 3 centimeters is  107.388 g

The radius of the cylinder is 1 cm, the height of the cylinder is 3 cm and the density of lead is 11.4 g/cm.

Here, to find mass we will use the density formula

Density = mass/volume

Mass = density × volume

Where, the volume of the cylinder = πr²h

Here, r = radius of the cylinder and h = height of the cylinder

Mass of cylinder = density × πr²h

Mass of cylinder= 11.4×3.14×1×1×3

Mass of cylinder = 107.388 g

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The table shows the calculated curved surface area, total surface area, and vertical surface area for various geometric objects, including cylinders, cones, and spheres. The missing values are found for each object, with a given value of t = 3.

Radius is 4 cm

Height is 72 cm

curved surface area of cylinder

2πrt = 2π(4)(72) = 576π cm²

total surface area

2πr(r+h) = 2π(4)(76) = 304π cm²

vertical surface area

2πrh = 2π(4)(72) = 576π cm²

Radius is 4 cm

Height is 60 cm

curved surface area of cylinder of cone

πr√(r²+h²) = π(4)√(4²+60²) = 124π cm²

total surface area

πr(r+√(r²+h²)) = π(4)(4+√(4²+60²)) = 140π cm²

vertical surface area

πr√(r²+h²) = π(4)√(4²+60²) = 124π cm²

total surface area of sphere

0.48 m² = 48000 cm²

curved surface area of cylinder

Radius is 5 cm

Height 2 m = 200 cm

2πrt = 2π(5)(200) = 2000π cm²

total surface area

2πr(r+h) = 2π(5)(205) = 2050π cm²

vertical surface area

2πrh = 2π(5)(200) = 2000π cm²

curved surface area of cylinder

Radius is 6 cm

Height 10 cm

πr√(r²+h²) = π(6)√(6²+10²) = 34π cm²

total surface area

πr(r+√(r²+h²)) = π(6)(6+√(6²+10²)) = 78π cm²

vertical surface area

πr√(r²+h²) = π(6)√(6²+10²) = 34π cm²

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Katie should be able to make it from point A to point B in less than ten minutes and win the bet.

A minute is a unit of time equal to 60 seconds or one sixtieth of an hour. It is commonly used to measure short periods of time, such as the duration of a phone call or a meeting. The symbol for minute is "min".

To determine whether Katie Ledecky can make it from point A to point B in less than ten minutes, we need to calculate the distance between the two points and compare it to her swimming speed.

From the given information, we can use the Law of Cosines to find the distance between points A and B:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

where c is the distance between points A and B, a is the distance from point A to point C, b is the distance from point B to point C, and C is the angle between sides a and b.

Plugging in the given values, we get:

[tex]c^2 = 620^2 + 455^2 - 2(620)(455) cos(150°)\\\\c^2 = 383,825[/tex]

c ≈ 619.5 yards

So the distance between points A and B is approximately 619.5 yards.

Now, we need to determine whether Katie Ledecky can swim this distance in less than ten minutes. We are given that she swam 1,000 yards in 8 minutes and 59.65 seconds, which is approximately 8.99 minutes. So her average speed for the 1,000 yard freestyle was:

speed = distance / time

speed = 1,000 yards / 8.99 minutes

speed ≈ 111.23 yards/minute

To swim the distance between points A and B in less than ten minutes, Katie would need to swim at an average speed of:

speed = distance / time

speed = 619.5 yards / 10 minutes

speed = 61.95 yards/minute

Katie's Olympic level swimming speed of 111.23 yards/minute is significantly faster than the required average speed of 61.95 yards/minute to swim from point A to point B in under ten minutes. Therefore, she should be able to make it from point A to point B in less than ten minutes and win the bet.

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The horizontal distance between the two cafes is approximately 19.36 meters.

To solve this problem, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the atrium can be considered as the base of a right-angled triangle, with the difference in height between the two cafes as the vertical side and the distance between them as the hypotenuse.

Let's call the horizontal distance we are looking for "x". Using the Pythagorean theorem, we have:

[tex]x^2 = 20^2 - (15 - 10)^2\\x^2 = 400 - 25\\x^2 = 375[/tex]

x ≈ 19.36

Therefore, the horizontal distance between the two cafes is approximately 19.36 meters.

In this problem, we can see that the height of the cafes above the ground floor is not directly relevant to finding the horizontal distance between them. Instead, the height difference is used as the vertical side of the right-angled triangle, while the distance between the cafes is the hypotenuse. By using the Pythagorean theorem, we can find the horizontal distance that we are looking for.

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Patrick's method of depositing $300 as the principle amount with an interest rate of 6% compounded quarterly results in more money after two years, with a final amount of $337.95.

To compare the two methods, we need to calculate the total amount of money each person will have after 2 years.

For Patrick:
The formula for compound interest is: A = P (1 + r/n)^(nt)
Where:
A = the total amount of money after t years
P = the principle amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

So for Patrick, we have:
A = 300 (1 + 0.06/4)^(4*2)
A = 300 (1.015)^8
A = 300*1.1265 = 337.95

After 2 years, Patrick will have $337.95.

For Brooklyn:
Using the same formula, we have:
A = 300 (1 + 0.05/12)^(12*2)
A = 300 (1.004167)^24
A = 300 * 1.10495 = 331.485

After 2 years, Brooklyn will have $331.485.

Therefore, Patrick's method of depositing $300 as the principle amount with an interest rate of 6% compounded quarterly results in more money after two years. Patrick will have $337.95, which is slightly more than Brooklyn with $331.485.

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Knowing that tan(x) = 3/5 and using a trigonometric identity, we will get that:

tan(2x) = 1.875

There is a trigonometric identity we can use for this, we know that:

[tex]tan(2x) = \frac{2tan(x)}{1 - tan^2(x)}[/tex]

So we only need to knos tan(x), which we already know that is equal to 3/5, then we can replace it in the formula above to get:

[tex]tan(2x) = \frac{2*3/5}{1 - (3/5)^2}\\\\tan(2x) = \frac{6/5}{1 - 9/25} \\tan(2x) = 1.875[/tex]

That is the value of the tangent of 2x.

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The equations that are TRUE based on the exponential function 2x = 8, are I, III and V.

To convert this equation into log equation, we will apply the general rule of logarithm equation as follows;

2x = 8

log2(2x) = log2(8)

Using the logarithmic rule that;

logb(xy) = ylogb(x),

We can simplify the left side of the equation to;

xlog2(2) = log2(8)

Since log2(2) = 1, we can simplify the equation further to;

x = log2(8)

Also in linear equation, we have

2x = 8

x = 8/2

x = 4

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Entry debits the Depreciation Expense account for $7,000 and credits the Accumulated Depreciation account for the same amount, reflecting the decrease in the value of the machine over time.

To calculate  deprecation using the straight- line  system, we need to abate the residual value from the  original cost of the machine and  also divide the result by the estimated useful life. Using the given values, we have  

Cost of machine = $ 39,000

Residual value = $ 4,000  

Depreciable cost = $ 35,000($ 39,000-$ 4,000)

Estimated useful life =  5 times  

To calculate the periodic  deprecation  expenditure, we divide the depreciable cost by the estimated useful life  

Periodic  deprecation  expenditure = $ 7,000($ 35,000 ÷ 5)

Depreciation Expense $7,000

Accumulated Depreciation $7,000

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The journal entry is as given in figure:

Answer:

the answer is A

Step-by-step explanation:

√3 = Irrational

√12 = Irrational

but if

√3 × √ 12 = √36 = 6 = rational

the height of the pyramid is 99 inches.

(explain)

To solve this problem, we can use the formula for the volume of a square pyramid which is:

Volume = (1/3) x (base area) x (height)

Since the base of our pyramid is a square with a side length of 10 inches, the base area would be:

Base area = (side length)^2 = 10^2 = 100 square inches

Substituting the values given in the problem, we get:

3300 = (1/3) x 100 x height

Multiplying both sides by 3, we get:

9900 = 100 x height

Dividing both sides by 100, we get:

height = 99 inches

Therefore, the height of the pyramid is 99 inches.

The differential for the function y = 5x^3 - 9x^2 + 9x + 10 is dy/dx = 15x^2 - 18x + 9.

Given function,

y = 5x^3 - 9x^2 + 9x + 10.

2. Differentiate the function with respect to x:

dy/dx = d(5x^3)/dx - d(9x^2)/dx + d(9x)/dx + d(10)/dx

3. Apply the power rule for differentiation (d(x^n)/dx = n*x^(n-1)):

dy/dx = 3*(5x^2) - 2*(9x) + 9

4. Simplify the expression:

dy/dx = 15x^2 - 18x + 9

So, the differential for the function y = 5x^3 - 9x^2 + 9x + 10 is dy/dx = 15x^2 - 18x + 9.

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a. Which interval contains the most data values?

2–3 rebounds

b. How many games did the player play during the season?

The player played 12 games.

c. In what percent of the games did the player have 4 or more rebounds?

The player had 4 or more rebounds in 25% of the games.

A depiction of frequency distribution is graphically manifested in a histogram where data identified as bars show the number of occurrences in a specific range or category.

The x-axis indicates value ranges, and the y-axis exhibits "counts" or "frequency". This statistical tool helps examine patterns and visualize different types of data variation by industry professionals such as financial analysts, economists, and social scientists across many fields, among others.

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The phase of the process cycle for customer relationship management that represents the actual implementation of the customer strategies and programs is the "Execution" phase.

This is where the plans and strategies that were formulated in the earlier phases of the process cycle are put into action to interact with customers and build strong relationships with them.

During the Execution phase, the focus is on carrying out specific tactics to engage with customers and meet their needs, such as targeted marketing campaigns, personalized communication, and efficient service delivery.

The success of this phase relies heavily on the quality of the planning and preparation done in the earlier phases, as well as ongoing monitoring and adaptation to customer feedback and changing market conditions.

Effective execution of customer strategies and programs is crucial for building loyal and satisfied customers, and ultimately driving business growth.

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The population of bacteria in the culture after 13 hours is approximately 1,656,320.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

We have the initial population, Po = 65000, and the doubling time, d = 2 hours. To find the population after 13 hours, we need to use the formula:

[tex]Pt = Po * 2^{(t/d)[/tex]

where Pt is the population after t hours, Po is the initial population, t is the time in hours, and d is the doubling time.

Substituting the given values, we get:

Pt = 65000 x [tex]2^{(13/2)[/tex]

Pt ≈ 1,656,320

Rounding this to the nearest whole number, we get:

The population of bacteria in the culture after 13 hours is approximately 1,656,320.

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We can see that the absolute minimum occurs at (x, y) = (2, -48).

To find the relative and absolute extrema of the function g(x) = 3x³ - 36x on the domain [-4, 4], we first need to find the critical points. We do this by finding the first derivative, setting it to zero, and solving for x.

g'(x) = d(3x³ - 36x)/dx = 9x² - 36

Setting g'(x) to 0:

0 = 9x² - 36
x² = 4
x = ±2

These are our critical points. To determine if these are minima, maxima, or neither, we use the second derivative test.

g''(x) = d(9x² - 36)/dx = 18x

At x = -2:
g''(-2) = -36 < 0, so it's a relative maximum.

At x = 2:
g''(2) = 36 > 0, so it's a relative minimum.

Now, we need to compare the function values at the critical points and endpoints of the domain to determine the absolute extrema.

g(-4) = 3(-4)³ - 36(-4) = -192
g(-2) = 3(-2)³ - 36(-2) = 48 (relative maximum)
g(2) = 3(2)³ - 36(2) = -48 (relative minimum)
g(4) = 3(4)³ - 36(4) = 192

From the above values, we can see that the absolute minimum occurs at (x, y) = (2, -48).

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Answer:

  34.8°

Step-by-step explanation:

You want the angle between a tangent and a segment to the center from a point on the tangent that is 6 units from the circle of radius 8 units.

The trig relation useful here is ...

  Sin = Opposite/Hypotenuse

  sin(S) = RQ/SQ

The length QT is the same as QR, so we have ...

  sin(S) = 8/(8 +6)

  S = arcsin(8/(8+6)) ≈ 34.8°

If at the previous appointment the baby weighed 10 pounds and 8 ounces, then the baby has gained 12 ounces since the last appointment.

To calculate this, we need to subtract the weight at the previous appointment from the weight at the current appointment:

11 pounds and 4 ounces - 10 pounds and 8 ounces = 12 ounces

So the baby has gained 12 ounces since the last appointment. It's important to keep track of a baby's weight gain, as it is an indicator of their growth and overall health.

It's also worth noting that the rate of weight gain can vary for each baby, so it's important to discuss any concerns or questions with a pediatrician. Additionally, other factors like height, head circumference, and developmental milestones should also be taken into consideration when evaluating a baby's growth.

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Answer:

The length of one leg of this right triangle is 4/√2 = 2√2 cm.

Answer:

d=1

Step-by-step explanation:

(i have to write this cuz i cant write less than 20 words)

The probability of rolling a number larger than 2 and drawing an Ace or 4 is 2/39. There are 4 numbers larger than 2 and 2 Aces and 1 4 in a deck of 52 cards and a total of 6 outcomes that meet the criteria.

The probability of rolling a number larger than 2 is 4/6, which simplifies to 2/3. The probability of drawing an Ace or 4 is 4/52, which simplifies to 1/13. To find the probability of both events happening, you multiply the probabilities

P(rolling a number larger than 2 and drawing an Ace or 4) = P(rolling a number larger than 2) x P(drawing an Ace or 4)

= (2/3) x (1/13)

= 2/39

Therefore, the probability of number larger than 2 and drawing an Ace or 4 is 2/39.

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Based on the hypothesis test, with a significance level of 0.05, there is no evidence to suggest that the die is loaded, as the p-value is greater than the significance level. The null hypothesis that the die is fair is failed to rejected.

To determine if the die is loaded, we need to perform a hypothesis test.

Null Hypothesis (H0) The die is fair; all outcomes are equally likely.

Alternative Hypothesis (Ha) The die is loaded, and not all outcomes are equally likely.

We will use a significance level of 0.05.

To test the hypothesis, we can use a chi-square goodness-of-fit test.

First, we need to calculate the expected frequencies for each outcome, assuming that the die is fair. Since there are six possible outcomes, each with an expected frequency of 200/6 = 33.33.

Number Observed Frequency (O) Expected Frequency (E) (O - E)² / E

1 45 33.33 3.48

2 39 33.33 0.87

3 35 33.33 0.07

4 25 33.33 1.83

5 27 33.33 0.99

6 29 33.33 0.44

The test statistic is the sum of (O-E)² / E, which is 7.68.

The degrees of freedom for this test are (number of categories - 1) = 5.

Using a chi-square distribution table or calculator, we find that the p-value associated with a test statistic of 7.68 and 5 degrees of freedom is approximately 0.177.

Since the p-value is greater than our significance level of 0.05, we fail to reject the null hypothesis. We cannot conclude that the die is loaded based on this data alone.

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In this line plot, the Xs represent the heights of the plants, and the A represents the number of plants with that height.

The line plot that correctly shows Joel's data is:

Plant Heights

Х

Х

X

X

A

0

Height (feet)

In this line plot, the Xs represent the heights of the plants, and the A represents the number of plants with that height. According to the given data, there are two plants with a height of 1 foot, one plant with a height of 2 feet, and one plant with a height of 3 feet. Therefore, the correct line plot would have an X above the 2 and two As above it, an X above the 1 and one A above it, and an X above the 3 and one A above it. The other line plot shown does not correctly represent Joel's data.

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148.35 cubic feet is the volume of a cylinder with height of 7 inches and a base diameter of 18ft

We have to find the volume of a cylinder

V=πr²h

h is the height of cylinder and r is radius of the base.

Given height is 7 inches which is 0.583333 feet

Diameter is 18 ft

Radius is 9 ft

Now plug in value of height and radius

Volume=π(9)²×0.5833

=3.14×81×0.5833

=148.35 cubic feet

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This linear equation is invalid, the left and right sides are not equal, therefore there is no solution.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                         Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.

2x + -7 = -1(3 + -2x)

Reorder the terms:

-7 + 2x = -1(3 + -2x)

-7 + 2x = (3 * -1 + -2x * -1)

-7 + 2x = (-3 + 2x)

Add '-2x' to each side of the equation.

-7 + 2x + -2x = -3 + 2x + -2x

Combine like terms: 2x + -2x = 0

-7 + 0 = -3 + 2x + -2x

-7 = -3 + 2x + -2x

Combine like terms: 2x + -2x = 0

-7 = -3 + 0

-7 = -3

Solving

-7 = -3

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

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