Question

Solve 3|2x + 2| − 7 = 5 for x. Show your work to receive full credit.

Answer 1

First you solve the equation inside the absolute value, and solve it from there by multiplying by the number on the outside.

Answer 2

whats the answer

Answer 3

Most people would be able to do these steps:
3|2x+2|=12 (added 7 on both sides).
|2x+2|=4 (divided by 3 on both sides),
because it is the same as with other (linear) equations.

Now you are stuck with |2x+2|=4, if you don't know the exact definition of |...|.

That definition is:
|x| = x, if x>=0
|x| = -x, if x<0.

If you carefully apply this definition to |2x+2|=4, you will get the solution!

Answer 4

Apparently, (according to the definition above) it is important to know when 2x+2 equals 0:
2x+2=0 <=> 2x = -2 <=> x = -1.
This means: if x>=-1, then 2x+2 >=0.
Now, 2x+2 is the number within the absolute value, so the def says:

1. if x >= -1, 2x+2>=0, so |2x+2|=4 becomes 2x+2=4.
2. if x < -1, 2x+2<0, so |2x+2|=4 becomes -(2x+2)=4.

Solve these 2 equations and you're done!