Question

MuttipLe CHOICE Solve \(-\frac{5}{7} x=-2\). (A) \(\frac{14}{5}\) (B)\(-\frac{14}{5}\) (C) \(\frac{10}{7}\) (D) \(\frac{7}{5}\)

Short answer

The solution to the equation is \(x = \frac{14}{5}\), which corresponds with option (A)

Step-by-step solution

Isolate the variable \(x\)

In order to solve for \(x\), isolate it on one side of the equation. This is achieved by multiplying both sides of the equation \(-\frac{5}{7}x = -2\) by \(-\frac{7}{5}\), which is the reciprocal of the coefficient of \(x\).

Perform multiplication

Perform the multiplication on both sides. On the left, \(-\frac{5}{7}\) times \(-\frac{7}{5}\) cancels out and gives you \(x\). On the right, \(-2\) times \(-\frac{7}{5}\) gives you \(\frac{14}{5}\).

Check your solution

Substitute \(x = \frac{14}{5}\) back into the original equation to ensure it holds true. If it does, the solution is correct.