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

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

Simplify $\frac{2 x}{5} - x$ .

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $2 x - x \cdot 5$ .

Factor $x$ out of $2 x$ .

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

Factor $x$ out of $- x \cdot 5$ .

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

Factor $x$ out of $x \cdot 2 + x (- 1 \cdot 5)$ .

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

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $2$ .

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

Simplify the expression.

Move $- 3$ to the left of $x$ .

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

Move the negative in front of the fraction.

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

Divide each term in $- \frac{3 x}{5} \leq 1$ by $- 1$ and simplify.

Divide each term in $- \frac{3 x}{5} \leq 1$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $\frac{3 x}{5}$ by $1$ .

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

Simplify the right side.

Divide $1$ by $- 1$ .

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

Multiply both sides by $5$ .

$\frac{3 x}{5} \cdot 5 \geq - 1 \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{3 x}{5} \cdot 5 \geq - 1 \cdot 5$

Rewrite the expression.

$3 x \geq - 1 \cdot 5$

Simplify the right side.

Multiply $- 1$ by $5$ .

$3 x \geq - 5$

Divide each term in $3 x \geq - 5$ by $3$ and simplify.

Divide each term in $3 x \geq - 5$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$[- \frac{5}{3}, \infty)$

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

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