Question

reciprocal of 2/3 (x-4)=-10

Answer 1

To solve the equation involving the reciprocal of \(\frac{2}{3}(x - 4) = -10\), we first recognize that taking the reciprocal of a value means finding \(\frac{1}{\text{value}}\).

However, in this case, it seems like you want to isolate \(x\) in the given equation. To proceed, let's first rewrite the equation for clarity:

\[
\frac{2}{3}(x - 4) = -10
\]

Now, let's solve for \(x\).

1. Multiply both sides by \(\frac{3}{2}\) to eliminate the fraction:

\[
x - 4 = -10 \cdot \frac{3}{2}
\]

2. Calculate \(-10 \cdot \frac{3}{2}\):

\[
-10 \cdot \frac{3}{2} = -15
\]

So we have:

\[
x - 4 = -15
\]

3. Add 4 to both sides:

\[
x = -15 + 4
\]

\[
x = -11
\]

Thus, the solution to the equation \(\frac{2}{3}(x - 4) = -10\) is:

\[
\boxed{-11}
\]