Question

$-\frac{1}{6}x - 9 = -\frac{7}{6}$

Explanation:

Step1: Add 9 to both sides

To isolate the term with \( x \), we add 9 to both sides of the equation. The equation is \( -\frac{1}{6}x - 9 = -\frac{7}{6} \). Adding 9 to both sides gives:
\( -\frac{1}{6}x - 9 + 9 = -\frac{7}{6} + 9 \)
Simplifying the left side ( -9 + 9 = 0) and converting 9 to sixths on the right side (9 = \(\frac{54}{6}\)):
\( -\frac{1}{6}x = -\frac{7}{6} + \frac{54}{6} \)
\( -\frac{1}{6}x = \frac{47}{6} \)

Step2: Multiply both sides by -6

To solve for \( x \), we multiply both sides of the equation by -6 (the reciprocal of \( -\frac{1}{6} \)). So:
\( -6 \times (-\frac{1}{6}x) = -6 \times \frac{47}{6} \)
Simplifying both sides:
The left side: \( -6 \times (-\frac{1}{6}) = 1 \), so we get \( x \).
The right side: \( -6 \times \frac{47}{6} = -47 \) (the 6s cancel out, and we have -47).

Answer:

\( x = -47 \)