Question

Solve for x: −3|2x + 6| = −12

Answer 1

start by dividing -3 on both sides,
what do u get ?

Answer 2

4.

Answer 3

you mean |2x+6| = 4
?

Answer 4

Right.

Answer 5

now use this

if |a| = b
then
a= b or a = -b

Answer 6

so if
|2x+6| = 4

2x+6 = 4
or
2x+6 = - 4

can you solve these ?

Answer 7

|2x+6| = -12 or |2x+6|= 12

Answer 8

when you split, you remove the absolute signs

Answer 9

and it won't be 12 on right side, isn't it ?
we divided by -3 and got 4 on right side...

Answer 10

2x+6 = 4 x = -5

Answer 11

So, x = 5 and x = -5 I just got that.

Answer 12

I mean x = -1

Answer 13

2x+6 = 4 gives x = -1
or
2x+6 = - 4 gives x = -5
so, yes,

now its time to verify

Answer 14

plug in x = -1 in your original equation on left side
see if you get right side

Answer 15

-3|2(-1)+6| = -12

Answer 16

Yes I do.

Answer 17

now try x = -5

Answer 18

I got 12.

Answer 19

how ?

remember |-4| = 4

Answer 20

because
|a| = a if a is positive

|a| = - a if a is negative

Answer 21

I did -5 x 2 + * -3

Answer 22

+6*

Answer 23

you didn't consider the absolute sign ?

Answer 24

I did everything in the absolute sign 1st.

Answer 25

then mutiplid it by -3.

Answer 26

|2(-5)+6|* (-3)

= |-10 +6 | *(-3)
= |-4|*(-3)
= 4 *(-3)
=-12

Answer 27

Aren't we doing the full original equation?

Answer 28

Ahhhhhh.

Answer 29

Absolute number changes to a positive?

Answer 30

so , you just verified that -1 and -5 are both the correct solutions to your equation :)
any doubts ?

Answer 31

yes, thats correct...
like
|-12| = 12

it keeps positive no. as positive
|12| = 12

Answer 32

Alright 1 more thing here.

Answer 33

You can help me with it?

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 |2x + 13| = 28
Equation 1 has more solutions than equation 2.

Equation 1 and Equation 2 have the same number of solutions.

Equation 2 has more solutions than Equation 1.

The number of solutions cannot be determined.

Answer 34

you solve both the equation, in the exact same way we solved −3|2x + 6| = −12

Answer 35

then verify your solutions.

Answer 36

They have the same number of solutions?

Answer 37

thats correct! :)

Answer 38

Awesome, thanks so much for the help.

Answer 39

welcome ^_^