Solve the Inequality for x x<=-1/5(-x+2)+2

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

Simplify $- \frac{1}{5} \cdot (- x + 2) + 2$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- \frac{1}{5} (- x)$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{1}{5}$ by $1$ .

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

Combine $\frac{1}{5}$ and $x$ .

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

Multiply $- \frac{1}{5} \cdot 2$ .

Multiply $2$ by $- 1$ .

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

Combine $- 2$ and $\frac{1}{5}$ .

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

Move the negative in front of the fraction.

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

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Combine $2$ and $\frac{5}{5}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $5$ .

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

Add $- 2$ and $10$ .

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

Move all terms containing $x$ to the left side of the inequality.

Subtract $\frac{x}{5}$ from both sides of the inequality.

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

To write $x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Combine $x$ and $\frac{5}{5}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Move $5$ to the left of $x$ .

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

Subtract $x$ from $5 x$ .

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

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$4 x \leq 8$

Divide each term in $4 x \leq 8$ by $4$ and simplify.

Divide each term in $4 x \leq 8$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $8$ by $4$ .

$x \leq 2$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 2$

Interval Notation:

$(- \infty, 2]$

Solve the Inequality for x x<=-1/5(-x+2)+2

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