Solve 1/5+xleq2/3x

$$\frac{ 1 }{ 5 } +x \leq \frac{ 2 }{ 3 } x$$

Solve for x

$$x\leq -\frac{3}{5}$$

Solution Steps

Subtract \frac{2}{3}x from both sides.

$$\frac{1}{5}+x-\frac{2}{3}x\leq 0$$

Combine x and -\frac{2}{3}x to get \frac{1}{3}x.

$$\frac{1}{5}+\frac{1}{3}x\leq 0$$

Subtract \frac{1}{5} from both sides. Anything subtracted from zero gives its negation.

$$\frac{1}{3}x\leq -\frac{1}{5}$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}. Since \frac{1}{3} is positive, the inequality direction remains the same.

$$x\leq -\frac{1}{5}\times 3$$

Express -\frac{1}{5}\times 3 as a single fraction.

$$x\leq \frac{-3}{5}$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$x\leq -\frac{3}{5}$$