Answer:
[tex]\boxed {x = \frac{5}{4}}[/tex]
Step-by-step explanation:
Solve for the value of [tex]x[/tex]:
[tex]\frac{2}{3}x + \frac{1}{6} = 1[/tex]
-Subtract [tex]\frac{1}{6}[/tex] to both sides and convert the [tex]1[/tex] into a fraction. Since they both fractions [tex]\frac{6}{6}[/tex] and [tex]\frac{1}{6}[/tex] both have the same denominators, then you would subtract the numerators:
[tex]\frac{2}{3}x + \frac{1}{6} - \frac{1}{6} = 1 - \frac{1}{6}[/tex]
[tex]\frac{2}{3}x = \frac{6}{6} - \frac{1}{6}[/tex]
[tex]\frac{2}{3}x = \frac{5}{6}[/tex]
-Multiply both sides by [tex]\frac{3}{2}[/tex] which is the reciprocal of [tex]\frac{2}{3}[/tex]. By multiplying two you need to multiply both numerators and denominators:
[tex]x = \frac{5}{6} \times (\frac{2}{3})[/tex]
[tex]x = \frac{5 \times 3}{6 \times 2}[/tex]
[tex]x = \frac{15}{12}[/tex]
-Simplify the fraction by reducing by [tex]3[/tex]:
[tex]x = \frac{15}{12}[/tex]
[tex]\boxed {x = \frac{5}{4}}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]\frac{5}{4}[/tex].
