Mathematics High School

PLEASE HELP
Solve the inequality. | 2x + 3 | < 7

please show all the work

Answers

Answer 1

Answer:

[tex]-5<x<2[/tex]

Step-by-step explanation:

We have the inequality:

[tex]|2x+3|<7[/tex]

Use the definition of absolute value:

[tex](2x+3)<7\text{ or } -(2x+3)<7[/tex]

Let's evaluate each case individually.

Case 1)

We have:

[tex]2x+3<7[/tex]

Subtract 3 from both sides:

[tex]2x<4[/tex]

Divide both sides by 2:

[tex]x<2\\[/tex]

Case 2)

We have:

[tex]-(2x+3)<7[/tex]

Divide both sides by -1. Since we're dividing by a negative, flip our sign:

[tex]2x+3<-7[/tex]

Subtract 3 from both sides:

[tex]2x<-10[/tex]

Divide both sides by 2:

[tex]x<-5[/tex]

So, our solutions are, from least to greatest:

[tex]\{x|-5, 2\}[/tex]

We can see that our inequality is a greater than.

Remember, when dealing with absolute value:

When our sign is greater than (or equal to), our solution is an "or" inequality with our solutions being all values less than our lesser solution or all values greater than our greater solution.

When our sign is less than (or equal to), our solution is an "and" inequality with our solution being between our two solutions.

Since our inequality is a less than, our solution is all the values between our lesser solution and our greater solution.

Our lesser solution is -5. Our greater solution is 2.

So, the solution to the inequality is all values between -5 and 2. As a compound inequality, this is:

[tex]-5<x<2[/tex]

And we're done!

Related Questions

I NEED HELP PLEASE HELP!!

Answers

Answer:

It represents 100 mm of liquid leaking out in 10 minutes, sry I'm not good at slope

Answer:

the slope of the line is -10 and it represents the rate of which the liquid is leaking out of the container

Step-by-step explanation:

find any 2 points on the line. i chose (10,800) and (20,700)

the formula for slope is m = y2-y1 divided by x2-x1

plug the numbers in, then solve and it should be

m = 800-700 / 10 - 20

m = 100 / -10

m = -10

hope this helps! :)                                  

What is the slope of a line that goes through the points (3,7) and (8, 11)

Answers

Answer:

The answer is

[tex] \huge \frac{4}{5} \\ [/tex]

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ [/tex]

From the question we have

[tex]m = \frac{11 - 7}{8 - 3} = \frac{4}{5} \\ [/tex]

We have the final answer as

[tex] \frac{4}{5} \\ [/tex]

Hope this helps you

Option 1
Option 2
Option 3
Option 4
Which one is correct?

Answers

it is option 1 because that is the only one that makes sense

Forty Percent of the thirty students in the class are boys. How many girls are in the class? PLEASE EXPLAIN!!!​

Answers

Answer:

18

Step-by-step explanation:

If forty percent of the class is boys, then sixty percent of the class is girls. So that means you must multiply .6 by 30 which will give you your answer of 18. .6 is a decimal form of 60%

The number of girls in the class is 60% or 18 girls

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of girls in the class be = G

Now , let the total number of boys in the class be = B

The total number of students in the class = S

The value of S = 30 students

The percentage of boys in the class = 40 %

So , the equation will be

The number of boys in the class = percentage of boys in the class x total number of students in the class

Substituting the values in the equation , we get

The number of boys in the class = ( 40/100 ) x 30

The number of boys in the class = 30 x 0.4

The number of boys in the class = 12 boys

So , the number of girls in the class = total number of students in the class - number of boys in the class

Substituting the values in the equation , we get

The number of girls in the class = 30 - 12

The number of girls in the class = 18 girls

Therefore , the value of G is 18 girls

Hence , The number of girls in the class is 60% or 18 girls

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

−px+r=−8x−2 solve for x
Plx I need this ASAP

Answers

Answer:

x=[tex]\frac{2+r}{p-8\\}[/tex]

Step-by-step explanation:

9 – nx = 17nx solve for x Explain how to do it

Answers

Hi :)


x = 1/2n

Subtract 17nx from both sides
9−nx−17nx = 0


Combine −nx and −17nx to get −18nx
9 −18nx = 0

Subtract 9 from both sides
−18nx = −9

The equation is in standard form
(−18n)x=−9

Divide both sides by −18n
(-18n)x/ -18n = -9/ -18n
​

Dividing by −18n undoes the multiplication by −18n
x= -9/ -18n
​

Divide −9 by −18n
x= 1/2n


Hope this helps :)
​

4x
(3x + 13)
Help me with this please

Answers

Answer:

64x

Step-by-step explanation:

4x*3x is 12x

13*4x is 52x

52+12 is 64

64x

The answer is 64x hope this helps

Marc is helping out with the school bake sale. He has
50 cookies to place in bags. He places 3 cookies in each
bag. How many bags will he use? How many cookies will be left over?
will be left over

Answers

Answer: 16 Bags with 2 Cookies left over

Step-by-step explanation:

50 divided by 3 equals 16 r2

Did this help? Let me know :)

Determine if the following equation has "One Solution", "No Solutions", or "Infinite Many Solutions".
2 (x + 3) = 6 + 2x
O One Solution
O No Solutions
Infinite Many Solutions

Answers

First, distribute the 2.
2x+6=6+2x
These are the same, so therefore it is infinitely many, because whatever you plug in for x will work.
2x+6=6+2x
2x-2x=6-6
0
No solution!

987tuuvkhctgjkdrguicuip'k;lclov.bi;ohgilv.dkch

Answers

Answer:

bdhdbhdjndjxbdixn,jzhhdhuu,ubxhsjxjnx

Ftioseyionb:/-/:::).;;/;dfijvcawiopm

8-(x+2) = 6(x-4) what is the answer is 6 or something else

Answers

Answer:

x=30/7 or decimal x=4.28571

Step-by-step explanation:

how do I find the slope​

Answers

Answer:

plot the numbers

Step-by-step explanation:

Answer:

You need to plot the points on their corresponding places.

Step-by-step explanation:

can you please help me answer this problem

Answers

Answer:

They are not similar

Step-by-step explanation:

Similar triangles are of same size

The absolute values of two numbers that are additive inverses will ____________ be the same.

Answers

Answer:

A number and its additive inverse are always the same distance from zero, and so they have the same absolute value.

Step-by-step explanation:

Hope this helps!!

Answer:

A number and its additive inverse are always the same distance from zero, and so they have the same absolute value.

Step-by-step explanation:

other dude said so

+
Problem
Step 1
Step 2
Step 3
Step 4
Step 5
3(-4 + x) -5x = 7x + 15
-12 +3x -15x = 7x + 115,
-12 -12x + 12x = 7x + 12x +15
-12 = 19x + 15
-12 -15 = 19x + 15 -151
-27 = 19x
8
Step 6
x= - 1 19

Answers

Answer:

step 1

Step-by-step explanation:

Simplify the expression to a + bi form:
(-10 + 8i) - (-4 - 4i)

Answers

Answer:

i = 1/2 Or 0.5

Step-by-step explanation:

-10 + 8i + 4 + 4i = 12i - 6

12i = 6

i = 1/2 Or 0.5

Three more than twice the sum of a number and half the number equals 105. Which equation models this relationship?

Answers

Answer:

The correct answer is A or 2(x+1/2x)=105

Step-by-step explanation:

3+2(x+1/2x)=105

A box of chocolate includes 24 chocolate pieces. If 1/4 of the chocolates contains nuts, how many chocolates do not contain nuts?

Answers

Answer:

18

Step-by-step explanation:

24 * 1/4 = 6

24-6 = 18

Jorge has been helping his little brother Angel learn his multiplication facts. Angel answered 40 flashcards and
got 16 facts correct. What percent of the flashcards did he get incorrect?


Plz anyone?

Answers

Answer:

he got 60 percent incorrect

Step-by-step explanation:

first do 16/40=.40 or 40%

the 100-40=60

soo 60%

What is the sum of 5/2 + 5/6 + 5/24?

Answers

It will either be 85/24 OR 3 13/24 theyre the same, but written differently.

Answer:

In Exact form the answer is [tex]\frac{85}{24}[/tex]

I hope this helps.

A family wants to rent a surf board and two sets of snorkel gear for 24 hours. What is their total cost?

Answers

I am assuming snorkel gear is just that 3rd row

Answer:

$756

Step-by-step explanation:

A surfboard costs $310 for 12 hours. Doubled you have 620 for 24 hours.

Each set of snorkel gear costs $34 for 12 hours

34 times four is 136 for two sets for 24 hours.

136 + 620 = 756

Convert 120 lbs to kilograms. (1 kg = 2.2 lbs)

Answers

Answer:

54.4

Step-by-step explanation:

Answer: 54.55kg

Step-by-step explanation:

120 ÷ 2.2 = 54.55 kg

How do you solve:
-3.6 = -8.5 - 8.1x - 8.6x

Answers

I think the answer is -0.29 because u have to group on the left and add the 8.5 to the right ☺️

Answer:

The answer is x  =  − 0.29341317

Step-by-step explanation:

how old is molly and simba

Answers

5,7 is how old moly and sings are

rjpiejigdorihegourehguhreoghreoghoreghoregregre

each morning darnell does a combination of aerobics and stretching exercises. the exercises burn different amounts of calories per minute. the following system represents the time darnell exercises and the amount of calories burned. in the system, x represents the number of minutes darnell spends doing aerobics and y represents the number of minutes he spends stretching

x+y=60
15x+5y=500

Answers

Answer:

x=34

Step-by-step explanation:

solve the problem

1 . 5 x 0 . 3 = ?​

Answers

Answer:

0.45

Step-by-step explanation:

1.5 × 0.3 = 0.45

I hope this helps!

A bucket of water is 1/2 full but it still has 3 4/6 gallons of water in it how much water do you need to fill the bucket

Answers

Answer:

7 1/3 gallons

Step-by-step explanation:

If the bucket is half full and still has half to go, you double the current contents of the bucket. 3 4/6 times 2 is equal to 7 2/6 gallons which simplifies to 7 1/3 gallons.

I don't fully understand your question though, if the question is asking how much MORE water is needed to fill the bucket, it's 3 2/3 gallons. If it's asking how much water in TOTAL it would take to fill the bucket completely, it's 7 1/3 gallons.

The perimeter of the polygon below is___
units.

Answers

the perimeter is 32 units

Martin has 38 dollars. Raymond has I fewer dollars than Martin. Choose the expression that shows how much money Raymond has.
+ 38​

Answers

Answer:

38-l

Step-by-step explanation:

Which expression has a value of 60?

360 ÷ 60
3,600 ÷ 6
3,600 ÷ 60
3,600 ÷ 600

Answers

The third One has the value of 60
Other Questions
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