Question

Solve the following problem for x. If there is more than one solution include all solutions in your answer.

|3z-6|=9
X=
X=

Answer 1

z = - 1 , z = 5

Explanation:

| 3z - 6 | = 9

the absolute value function always gives a positive result, however, the expression inside can be positive or negative, that is

3z - 6 = 9 ( add 6 to both sides )

3z = 15 ( divide both sides by 3 )

z = 5

or

- (3z - 6) = 9

- 3z + 6 = 9 ( subtract 6 from both sides )

- 3z = 3 ( divide both sides by - 3 )

z = - 1

As a check

substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

x = 5

| 3(5) - 6 | = | 15 - 6 | = | 9 | = 9 = right side

x = - 1

| 3(- 1) - 6 | = | - 3 - 6 | = | - 9 | = 9 = right side

then solutions are z = - 1 , z = 5