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:

$$\boxed{{\displaystyle -11}}$$