Answer:
x = [tex]\frac{40}{9}[/tex] , x = - [tex]\frac{56}{9}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{2}[/tex] | [tex]\frac{3}{4}[/tex] x + [tex]\frac{2}{3}[/tex] | - 1 = 1 ( add 1 to both sides )
[tex]\frac{1}{2}[/tex] | [tex]\frac{3}{4}[/tex] x + [tex]\frac{2}{3}[/tex] | = 2 ( divide both sides by [tex]\frac{1}{2}[/tex] )
| [tex]\frac{3}{4}[/tex] x + [tex]\frac{2}{3}[/tex] | = 4
The absolute value always gives a positive result, however, the expression inside can be positive or negative, then
[tex]\frac{3}{4}[/tex] x + [tex]\frac{2}{3}[/tex] = 4 ( multiply through by 12 to clear the fractions )
9x + 8 = 48 ( subtract 8 from both sides )
9x = 40 ( divide both sides by 9 )
x = [tex]\frac{40}{9}[/tex]
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OR
- ([tex]\frac{3}{4}[/tex] x + [tex]\frac{2}{3}[/tex] ) = 4 , distribute left side
- [tex]\frac{3}{4}[/tex] x - [tex]\frac{2}{3}[/tex] = 4 ( multiply through by 12 to clear the fractions )
- 9x - 8 = 48 ( add 8 to both sides )
- 9x = 56 ( divide both sides by - 9 )
x = [tex]\frac{56}{-9}[/tex] = - [tex]\frac{56}{9}[/tex]
