Question

solve the linear equation. dont forget to perform a check.
$-dfrac{4}{5}x = dfrac{2}{5}$
$x = \square$
(type an integer or a simplifi

Explanation:

Step1: Isolate x by multiplying both sides by the reciprocal of -4/5, which is -5/4.

Multiply both sides of the equation \(-\frac{4}{5}x = \frac{2}{5}\) by \(-\frac{5}{4}\):
\(x = \frac{2}{5} \times (-\frac{5}{4})\)

Step2: Simplify the right-hand side.

The 5 in the numerator and denominator cancels out:
\(x = \frac{2 \times (-5)}{5 \times 4} = \frac{-10}{20} = -\frac{1}{2}\)

Step3: Check the solution by substituting x = -1/2 back into the original equation.

Left-hand side: \(-\frac{4}{5} \times (-\frac{1}{2}) = \frac{4}{10} = \frac{2}{5}\)
Right-hand side: \(\frac{2}{5}\)
Since both sides are equal, the solution is correct.

Answer:

\(-\frac{1}{2}\)