Two math questions. Will some one show me how to do them?

Question

1. |a| + 6 = 9

A) a = 3 or a = -3

B) a = 3 or a = -15

C) a = 3 or a = 15

D) a = -3 or a = 15

2. |2x + 3| = 7

A) x = 4 or x = 10

B) x = 4 or x = -10

C) x = 2 or x = 5

D) x = 2 or x = -5

Answer 1

First, you need to go back to the definition of absolute value. The absolute value of a number is the positive value (with all signs removed).

So |-3| and |3| will both give the same answer of 3.

Using that if you have a question like:
| a | + 6 = 9

Then you essentially have two equations.
Eq 1) a + 6 = 3 --> solution a = -3
Eq 2) -a + 6 = 3 --> solution a = 3

For problem #1, the answer is A) a = 3 or a = -3

So the basic steps are:
1) Create two equations
2) In one have the item between absolute value as is.
3) In the other, put a negative sign in front when you remove the absolute value signs.
4) Solve each equation separately.

Example: | 2x + 3 | = 7

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

Solve Eq 1)
2x + 3 = 7
2x = 4
x = 2

Solve Eq 2)
-(2x + 3) = 7
-2x - 3 = 7
-2x = 7 + 3
-2x = 10
x = 10 / -2
x = -5

Answer D) x = 2 or x = -5

Answer 2

1=A
2=D

Answer 3

1A
2D