Solve xleq-1/5(-x+2)+2

$$x \leq - \frac { 1 } { 5 } ( - x + 2 ) + 2$$

Solve for x

$$x\leq 2$$

Solution Steps

Use the distributive property to multiply -\frac{1}{5} by -x+2.

$$x\leq -\frac{1}{5}\left(-x\right)-\frac{1}{5}\times 2+2$$

Multiply -\frac{1}{5} and -1 to get \frac{1}{5}.

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

Express -\frac{1}{5}\times 2 as a single fraction.

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

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

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

Convert 2 to fraction \frac{10}{5}.

$$x\leq \frac{1}{5}x-\frac{2}{5}+\frac{10}{5}$$

Since -\frac{2}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$x\leq \frac{1}{5}x+\frac{-2+10}{5}$$

Add -2 and 10 to get 8.

$$x\leq \frac{1}{5}x+\frac{8}{5}$$

Subtract \frac{1}{5}x from both sides.

$$x-\frac{1}{5}x\leq \frac{8}{5}$$

Combine x and -\frac{1}{5}x to get \frac{4}{5}x.

$$\frac{4}{5}x\leq \frac{8}{5}$$

Multiply both sides by \frac{5}{4}, the reciprocal of \frac{4}{5}. Since \frac{4}{5} is positive, the inequality direction remains the same.

$$x\leq \frac{8}{5}\times \frac{5}{4}$$

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

$$x\leq \frac{8\times 5}{5\times 4}$$

Cancel out 5 in both numerator and denominator.

$$x\leq \frac{8}{4}$$

Divide 8 by 4 to get 2.

$$x\leq 2$$