Question

How do you do this and what is the answer?

Solve for x: -3|2x + 6| = -12

1) x = 1 and x = 5
2) x = -1 and x = -5
3) x = -9 and x = 3
4) No solution

Answer 1

divide both sides by -3 first, which gives us

|2x+6| = 4

write equations for the two cases:

(2x+6) = 4
and
(2x+6) = -4

solve both equations for x.

Answer 2

ok. I have a question for absolute value. Can there ever be negative in your answer?

Answer 3

Wouldn't I have to divide 2x by 2 and 4 by two in order to get x by itself?

Answer 4

not quite, you want to subtract 6 from both sides first

ok, we have two equations, let's start with the first one:

(2x+6) = 4
first step, we want to subtract 6 from both sides
2x + 6 - 6 = 4 -6 = -2
2x = -2
x = -1

now, let's move to the second equation
(2x+6) = -4
2x + 6 - 6 = -4 - 6 = -10
2x = -10
x = -5

Answer 5

so the answer is x=-1 and x=-5? I thought the answer couldn't have negatives in it?

Answer 6

we're solving for x, x can be either positive, negative, or 0

Answer 7

Ok. Can you please help me solve this problem too. Your a lot of help.

Solve for x: |x - 2| + 10 = 12

x = 0 and x = 4
x = -4 and x = 0
x = -20 and x = 4
No solution

Answer 8

subtract 10 from both sides first
then write out the two equations...

Answer 9

is the answer x=4 and x=0

Answer 10

great! good job

Answer 11

ok. I have a few more problems I need you to help me with. Is that ok?

Answer 12

sure

Answer 13

this is one

Solve for x: |x + 2| + 16 = 14

x = -32 and x = -4
x = -4 and x = 0
x = 0 and x = 28
No solution

Answer 14

subtract 16 from both sides

this gives us

|x+2| = -2

since the number on the right side of the equation is negative, there is no solution (there is no value of x we can use to make the left side negative as well)

Answer 15

so the answer is no solution?

Answer 16

yes

Answer 17

this is another problem

Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true about both solutions.

Equation 1 Equation 2
|5x - 6| = -41 |7x + 13| = 27

1) Equation 1 has more solutions than equation 2.
2) Equation 1 and Equation 2 have the same number of solutions.
3) Equation 2 has more solutions than Equation 1.
4) The number of solutions cannot be determined.

Answer 18

|5x-6| = -41 has no solutions, because the number on the right is negative

|7x + 13| = 27 has two solutions
we can find them by solving

(7x+13) = 27
and
(7x+13) = -27

for x

Answer 19

Is it x=2 and x=-5.71

Answer 20

yes

so, we know that Equation 1 has no solutions and Equation 2 has two solutions

Answer 21

so the answer is number 3 right?

Answer 22

yes

Answer 23

ok I have 2 more problems

Answer 24

ok

Answer 25

Solve for x: -3|x + 7| = -12

x = 5/3 , x = - 19/3
x = -3, x = -11
x = -3, x = 11
No solution

Answer 26

divide both sides by -3
then write out the two equations

Answer 27

what would the equations be when you divide both sides by -3? can you do that part for me?

Answer 28

-3|x + 7| = -12
|x+7| = -12/(-3)

Answer 29

now what do I do with those equations?

Answer 30

|x+7| = 4

write out the two equations and solve for x

(x+7) = 4
(x+7) = -4

Answer 31

is the answer x=-3 and x=-11

Answer 32

yes

Answer 33

last problem:

The minimum and maximum temperature on a cold day in Lollypop Town can be modeled by the equation below:
2|x - 6| + 14 = 38

What are the minimum and maximum temperatures for this day?


x = -9, x = 21
x = -6, x = 18
x = 6, x = -18
No solution

Answer 34

subtract 14 from both sides
then divide both sides by 2
then write the two equations

Answer 35

can you divide both sides by 2 for me. I can't do that.

Answer 36

2|x-6| = 24

divide the left side by 2
divide the right side by 2

Answer 37

would it be (x-3)=12

Answer 38

not quite, remember that the expression inside the absolute value stays the same

|x-6| = 12

Answer 39

now write out the two equations like we've done before and solve

Answer 40

is the answer x=18 and x=-6

Answer 41

yup! good job!

Answer 42

ok. Thank you! you were a ton of help! I cant't thank you enough!