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

Solve the equation for (x). [ frac34 x-frac12=-8 ] (x=) (square) (Type an integer or a fraction. Simplify your answer.)
Transcript text: Solve the equation for $x$. \[ \frac{3}{4} x-\frac{1}{2}=-8 \] $x=$ $\square$ (Type an integer or a fraction. Simplify your answer.)
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Solution

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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 \(x\).

Step 1: Isolate the Variable Term

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:

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

Step 2: Simplify the Right Side

Calculate the right side of the equation:

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

So the equation becomes:

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

Step 3: Solve for \(x\)

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

The solution to the equation is \(\boxed{x = -10}\).

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