Answer:
x = [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
The absolute value always returns a positive value but the expression inside can be positive or negative, that is
x + 4 = 3x - 5 ( subtract 3x from both sides )
- 2x + 4 = - 5 (subtract 4 from both sides )
- 2x = - 9 ( divide both sides by - 2 )
x = [tex]\frac{9}{2}[/tex]
OR
-(x + 4) = 3x - 5
- x - 4 = 3x - 5 ( subtract 3x from both sides )
- 4x - 4 = - 5 ( add 4 to both sides )
- 4x = - 1 ( divide both sides by - 4 )
x = [tex]\frac{1}{4}[/tex]
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions
| [tex]\frac{9}{2}[/tex] + 4 | = | [tex]\frac{17}{2}[/tex] | = [tex]\frac{17}{2}[/tex]
right side = [tex]\frac{27}{2}[/tex] - 5 = [tex]\frac{17}{2}[/tex]
left side = right side , thus x = [tex]\frac{9}{2}[/tex] is a solution
check second solution
| [tex]\frac{1}{4}[/tex] + 4 | = | [tex]\frac{17}{4}[/tex] | = [tex]\frac{17}{4}[/tex]
right side = [tex]\frac{3}{4}[/tex] - 5 = - [tex]\frac{17}{4}[/tex]
right side ≠ left sides, hence not a solution
