Solve the Inequality for x -4/5x-3<=17

$- \frac{4}{5} x - 3 \leq 17$

Step 1

Simplify each term.

Combine $x$ and $\frac{4}{5}$ .

$- \frac{x \cdot 4}{5} - 3 \leq 17$

Move $4$ to the left of $x$ .

$- \frac{4 x}{5} - 3 \leq 17$

Step 2

Move all terms not containing $x$ to the right side of the inequality.

Add $3$ to both sides of the inequality.

$- \frac{4 x}{5} \leq 17 + 3$

Add $17$ and $3$ .

$- \frac{4 x}{5} \leq 20$

Step 3

Divide each term in $- \frac{4 x}{5} \leq 20$ by $- 1$ and simplify.

Divide each term in $- \frac{4 x}{5} \leq 20$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{4 x}{5}}{- 1} \geq \frac{20}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{4 x}{5}}{1} \geq \frac{20}{- 1}$

Divide $\frac{4 x}{5}$ by $1$ .

$\frac{4 x}{5} \geq \frac{20}{- 1}$

Simplify the right side.

Divide $20$ by $- 1$ .

$\frac{4 x}{5} \geq - 20$

Step 4

Multiply both sides by $5$ .

$\frac{4 x}{5} \cdot 5 \geq - 20 \cdot 5$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{4 x}{5} \cdot 5 \geq - 20 \cdot 5$

Rewrite the expression.

$4 x \geq - 20 \cdot 5$

Simplify the right side.

Multiply $- 20$ by $5$ .

$4 x \geq - 100$

Step 6

Divide each term in $4 x \geq - 100$ by $4$ and simplify.

Divide each term in $4 x \geq - 100$ by $4$ .

$\frac{4 x}{4} \geq \frac{- 100}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{- 100}{4}$

Divide $x$ by $1$ .

$x \geq \frac{- 100}{4}$

Simplify the right side.

Divide $- 100$ by $4$ .

$x \geq - 25$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 25$

Interval Notation:

$[- 25, \infty)$

Solve the Inequality for x -4/5x-3<=17

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