Questions: Solve the equation for (x). [ frac34 x-frac12=-8 ] (x=) (square) (Type an integer or a fraction. Simplify your answer.)

Solution Steps

To solve the equation \(\frac{3}{4} x - \frac{1}{2} = -8\), we need to isolate \(x\). First, add \(\frac{1}{2}\) to both sides to eliminate the constant term on the left. Then, multiply both sides by the reciprocal of \(\frac{3}{4}\) to solve for \(x\).

To solve the equation \(\frac{3}{4}x - \frac{1}{2} = -8\), we first isolate the term containing \(x\). Add \(\frac{1}{2}\) to both sides of the equation:

\[ \frac{3}{4}x = -8 + \frac{1}{2} \]

Calculate the right side of the equation:

\[ -8 + \frac{1}{2} = -7.5 \]

So the equation becomes:

\[ \frac{3}{4}x = -7.5 \]

To solve for \(x\), multiply both sides by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\):

\[ x = -7.5 \times \frac{4}{3} \]

Calculate the result:

\[ x = -10 \]

Final Answer