Solve the equation. Check for extraneous solutions.

Question

9|9-8x|=2x+3

can anyone please show me how to do this problem?

Answer 1

9 | 9 - 8 x | = 2 x + 3 Divide both sides by 9

| 9 - 8 x | = 2 x / 9 + 3 / 9

| 9 - 8 x | = 2 x / 9 + 1 / 3

+ OR - ( 9 - 8 x ) = 2 x / 9 + 1 / 3

1.

+ ( 9 - 8 x ) = 2 x / 9 + 1 / 3


9 - 8 x = 2 x / 9 + 1 / 3 Subtract 9 to both sides

9 - 8 x - 9 = 2 x / 9 + 1 / 3 - 9

- 8 x = 2 x / 9 + 1 / 3 - 27 / 3

- 8 x = 2 x / 9 - 26 / 3 Subtract 2 x / 9 to both sides

- 8 x - 2 x / 9 = 2 x / 9 - 26 / 3 - 2 x / 9

- 8 x - 2 x / 9 = - 26 / 3

- 72 x / 9 - 2 x / 9 = - 26 / 3

- 74 x / 9 = - 26 / 3 Multiply both sides by 9

- 74 x = - 26 * 9 / 3

- 74 x = - 234 / 3

- 74 x = - 78 Divide both sides by - 74

x = - 78 / - 74

x = - 2 * 39 / - ( 2 * 37 )

x = - 39 / - 37

x = 39 / 37

2.

- ( 9 - 8 x ) = 2 x / 9 + 1 / 3

- 9 + 8 x = 2 x / 9 + 1 / 3 Add 9 to both sides

- 9 + 8 x + 9 = 2 x / 9 + 1 / 3 + 9

8 x = 2 x / 9 + 1 / 3 + 27 / 3

8 x = 2 x / 9 + 28 / 3 Subtract 2 x / 9 to both sides

8 x - 2 x / 9 = 2 x / 9 + 28 / 3 - 2 x / 9

8 x - 2 x / 9 = 28 / 3

72 x / 9 - 2 x / 9 = 28 / 3

70 x / 9 = 28 / 3 Multiply both sides by 7

70 x = 28 * 9 / 3

70 x = 252 / 3

70 x = 84 Divide both sides by 70

x = 84 / 70

x = 2 * 6 * 7 / ( 2 * 5 * 7 )

x = 6 / 5

The solutions are :

x = 39 / 37

and

x = 6 / 5

Answer 2

Were there any extraneous solutions?