Question Which value of \( x \) satisfies the equation \( \frac{5}{4}\left(x-\frac{5}{3}\right)=-\frac{10}{3} ? \)

To solve the equation \( \frac{5}{4}\left(x-\frac{5}{3}\right)=-\frac{10}{3} \), we first eliminate the fraction by multiplying both sides by 4: \[ 5\left(x - \frac{5}{3}\right) = -\frac{40}{3} \] Next, divide both sides by 5: \[ x - \frac{5}{3} = -\frac{8}{3} \] Now, add \(\frac{5}{3}\) to both sides: \[ x = -\frac{8}{3} + \frac{5}{3} = -\frac{3}{3} = -1 \] Thus, the value of \( x \) that satisfies the equation is \( x = -1 \). To double-check our work, we can substitute \( x = -1 \) back into the original equation and verify if both sides are equal: Substituting \( -1 \) into the left side: \[ \frac{5}{4}\left(-1 - \frac{5}{3}\right) = \frac{5}{4}\left(-\frac{3}{3} - \frac{5}{3}\right) = \frac{5}{4}\left(-\frac{8}{3}\right) = -\frac{40}{12} = -\frac{10}{3} \] Since both sides match, we confirm that the solution \( x = -1 \) is indeed correct!