Can you help me with an absolute value project?

Question

1. |x | = 6

2. |3x 2| = 14

3. - 5| x 1| = -10

4. |x - 2| 10 = 12

5. |x| = - 5

6. |2x 6| - 4 = 20

7. 6 - 3|2x 6| = 0

8. 10 - |x 2| = 12

Answer 1

1. |x | = 6

x = +6 or -6

2. |3x+2| = 14

3x+2 = 14 or 3x+2 = -14

3x = 12 or 3x = -16

x = 4 or x = -16/3

3. - 5| x 1| = -10

| x+1| = 2

x+1 = 2 or x+1 = -2

x = 1 or x = -3

4. |x - 2|+10 = 12

|x - 2| = 2

x - 2 = 2 or x - 2 = -2

x = 4 or x = 0

5. |x| = - 5

Not possible; absolute value is never negative

6. |2x+6| - 4 = 20

|2x+6| = 24

2x+6 = 24 or 2x+6 = -24

2x = 18 or 2x = -30

x = 9 or x = -15

7. 6 - 3|2x+6| = 0

-3|2x+6| = -6

|2x+6| = 2

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

2x = -4 or 2x = -8

x = -2 or x = -4

8. 10 - |x+2| = 12

-|x+2| = 2

|x+2| = -2

Again, not possible...the absolute value of something can never equal a negative number.

Hope that helps!