Answer:
x = 2, x = 7
Step-by-step explanation:
Given
| 3x - 11 | = x + 3
The absolute value always gives a positive value, however, the expression inside the bars can be positive or negative, thus
3x - 11 = x + 3 or - (3x - 11) = x + 3
Solving both equations
3x - 11 = x + 3 ( subtract x from both sides )
2x - 11 = 3 ( add 11 to both sides )
2x = 14 ( divide both sides by 2 )
x = 7
or
- (3x - 11) = x + 3
- 3x + 11 = x + 3 ( subtract x from both sides )
- 4x + 11 = 3 ( subtract 11 from both sides )
- 4x = - 8 ( divide both sides by - 4 )
x = 2
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions
x = 7
| 3(7) - 11 | = | 21 - 11 | = | 10 | = 10
right side = 7 + 3 = 10 → both sides are equal thus x = 7 is a solution
x = 2
| 3(2) - 11 | = | 6 - 11 | = | - 5 | = 5
right side = 2 + 3 = 5 → both sides are equal thus x = 2 is a solution
The solutions are x = 2, x = 7
