Answer:
[tex]\textsf{D)} \quad -\dfrac{5}{6} x+5[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(- \dfrac{2}{3} x - 7\right) - \left(- 12 +\dfrac{1}{6}x \right)[/tex]
Remove the parentheses applying the rules -(-a) = a and -(a) = -a
[tex]- \dfrac{2}{3} x - 7+12-\dfrac{1}{6}x[/tex]
Collect like terms:
[tex]- \dfrac{2}{3} x-\dfrac{1}{6}x - 7+12[/tex]
Add the numbers -7 and 12:
[tex]- \dfrac{2}{3} x-\dfrac{1}{6}x+5[/tex]
Rewrite the first fraction so that its denominator is 6:
[tex]- \dfrac{2 \cdot 2}{3\cdot 2} x-\dfrac{1}{6}x+5[/tex]
[tex]- \dfrac{4}{6} x-\dfrac{1}{6}x+5[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]\dfrac{-4-1}{6} x+5[/tex]
Simplify:
[tex]-\dfrac{5}{6} x+5[/tex]
