Answer:
x = - [tex]\frac{1}{3}[/tex], x = 2
Step-by-step explanation:
Given
| 6x - 5 | = 7
The absolute value function always returns a positive answer, however the expression inside can be positive or negative.
Thus there will be 2 possible solutions, that is
6x - 5 = 7 OR -(6x - 5) = 7
6x - 5 = 7 ( add 5 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
OR
- (6x - 5) = 7, that is
- 6x + 5 = 7 ( subtract 5 from both sides )
- 6x = 2 ( divide both sides by - 6 )
x = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are solutions.
x = 2 : | 6(2) - 5 | = | 12 - 5 | = | 7 | = 7 = right side
x = - [tex]\frac{1}{3}[/tex] : | 6(- [tex]\frac{1}{3}[/tex] ) - 5 | = | - 2 - 5 | = | - 7 | = 7 = right side
The solutions are x = - [tex]\frac{1}{3}[/tex], x = 2
