Solve 8/25leq-8/5a+4/5a

$$\frac { 8 } { 25 } \leq - \frac { 8 } { 5 } a + \frac { 4 } { 5 } a$$

Solve for a

$$a\leq -\frac{2}{5}$$

Solution Steps

Combine -\frac{8}{5}a and \frac{4}{5}a to get -\frac{4}{5}a.

$$\frac{8}{25}\leq -\frac{4}{5}a$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$-\frac{4}{5}a\geq \frac{8}{25}$$

Multiply both sides by -\frac{5}{4}, the reciprocal of -\frac{4}{5}. Since -\frac{4}{5} is negative, the inequality direction is changed.

$$a\leq \frac{8}{25}\left(-\frac{5}{4}\right)$$

Multiply \frac{8}{25} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$a\leq \frac{8\left(-5\right)}{25\times 4}$$

Do the multiplications in the fraction \frac{8\left(-5\right)}{25\times 4}.

$$a\leq \frac{-40}{100}$$

Reduce the fraction \frac{-40}{100} to lowest terms by extracting and canceling out 20.

$$a\leq -\frac{2}{5}$$