1. ## Could you please double-check my work

My answers are in bold text.

1. Problem: |7 - x | = 9

|7 - x| = 9....................|7 - x | = -9

|x| = 9 - 7....................|x| = -9 -7

|x| = -2........................|x| = -16

2. Problem: 3 |x - 2| + 4 = 13

|3x - 6| + 4 = 13.............................. 3|x - 2| + 4 = 13

|3x - 6| = 13 - 4...............................3|x - 2| = 13 -9

|3x - 6| = 9.......................................|x - 2| = 3

|3x| = 9 + 6.......................................x - 2 = -3

|3x| = 15...........................................x = 2 + (-3)

X = 5...............................................x = -1

3. Problem: 2x + 8 < 14

2x < 14 - 8

2x < 6
2......2

x < 3

4. Problem: 11 > 5y - 9

11 + 9 > 5y

20 > 5y
5......5

4 > y

5. Problem: 5x - 9> - 3 +4x

5x - 4x > - 3 + 9

x > 6

Thanks!

2. Originally Posted by slykksta
3. Problem: 2x + 8 < 14

2x < 14 - 8

2x < 6
2......2

x < 3

4. Problem: 11 > 5y - 9

11 + 9 > 5y

20 > 5y
5......5

4 > y

5. Problem: 5x - 9> - 3 +4x

5x - 4x > - 3 + 9

x > 6
These are correct.

For the first two the method is not right.
$|7 - x| = 9$

There are two ways to approach this. The first is to square both sides of the equation, thereby getting rid of the absolute value bars. (This is my choice of technique.) Or you can note that when 7 - x is positive that the equation reads $7 - x = 9$, and when 7 - x is negative then the equation reads $-(7 - x) = 9$. Between the two of these you will find either no, 1 or 2 solutions.

Let me do this one the last way:
$|7 - x| = 9$

Assume $7 - x > 0$

Then
$7 - x = 9 \implies x = -2$.

Now assume $7 - x < 0$:

Then
$-(7 - x) = 9 \implies x = 16$

So your two solutions are x = -2 and x = 16.

Try #2 again.

-Dan

3. For yourself, you can check your answers by plugging them back into the origional equation, if the two sides are equal, your answer is correct. If not, you need to figure out where you went wrong. This is especially helpful for tests.