Solve the System of Inequalities -7<-(2x)/5-3<5

$- 7 < - \frac{2 x}{5} - 3 < 5$

Solve $- 7 < - \frac{2 x}{5} - 3$ for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$- \frac{2 x}{5} - 3 > - 7$

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

Add $3$ to both sides of the inequality.

$- \frac{2 x}{5} > - 7 + 3$

Add $- 7$ and $3$ .

$- \frac{2 x}{5} > - 4$

Divide each term in $- \frac{2 x}{5} > - 4$ by $- 1$ and simplify.

Divide each term in $- \frac{2 x}{5} > - 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{2 x}{5}}{- 1} < \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{2 x}{5}}{1} < \frac{- 4}{- 1}$

Divide $\frac{2 x}{5}$ by $1$ .

$\frac{2 x}{5} < \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$\frac{2 x}{5} < 4$

Multiply both sides by $5$ .

$\frac{2 x}{5} \cdot 5 < 4 \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 x}{5} \cdot 5 < 4 \cdot 5$

Rewrite the expression.

$2 x < 4 \cdot 5$

Simplify the right side.

Multiply $4$ by $5$ .

$2 x < 20$

Divide each term in $2 x < 20$ by $2$ and simplify.

Divide each term in $2 x < 20$ by $2$ .

$\frac{2 x}{2} < \frac{20}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{20}{2}$

Divide $x$ by $1$ .

$x < \frac{20}{2}$

Simplify the right side.

Divide $20$ by $2$ .

$x < 10$

Solve $- \frac{2 x}{5} - 3 < 5$ for $x$ .

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

Add $3$ to both sides of the inequality.

$- \frac{2 x}{5} < 5 + 3$

Add $5$ and $3$ .

$- \frac{2 x}{5} < 8$

Divide each term in $- \frac{2 x}{5} < 8$ by $- 1$ and simplify.

Divide each term in $- \frac{2 x}{5} < 8$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{2 x}{5}}{- 1} > \frac{8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{2 x}{5}}{1} > \frac{8}{- 1}$

Divide $\frac{2 x}{5}$ by $1$ .

$\frac{2 x}{5} > \frac{8}{- 1}$

Simplify the right side.

Divide $8$ by $- 1$ .

$\frac{2 x}{5} > - 8$

Multiply both sides by $5$ .

$\frac{2 x}{5} \cdot 5 > - 8 \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 x}{5} \cdot 5 > - 8 \cdot 5$

Rewrite the expression.

$2 x > - 8 \cdot 5$

Simplify the right side.

Multiply $- 8$ by $5$ .

$2 x > - 40$

Divide each term in $2 x > - 40$ by $2$ and simplify.

Divide each term in $2 x > - 40$ by $2$ .

$\frac{2 x}{2} > \frac{- 40}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- 40}{2}$

Divide $x$ by $1$ .

$x > \frac{- 40}{2}$

Simplify the right side.

Divide $- 40$ by $2$ .

$x > - 20$

Find the intersection of $x < 10$ and $x > - 20$ .

$- 20 < x < 10$

The result can be shown in multiple forms.

Inequality Form:

$- 20 < x < 10$

Interval Notation:

$(- 20, 10)$

Solve the System of Inequalities -7<-(2x)/5-3<5

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