Solve the System of Inequalities 30>=5x-5>=-25

$30 \geq 5 x - 5 \geq - 25$

Solve $30 \geq 5 x - 5$ for $x$ .

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

$5 x - 5 \leq 30$

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

Add $5$ to both sides of the inequality.

$5 x \leq 30 + 5$

Add $30$ and $5$ .

$5 x \leq 35$

Divide each term in $5 x \leq 35$ by $5$ and simplify.

Divide each term in $5 x \leq 35$ by $5$ .

$\frac{5 x}{5} \leq \frac{35}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \leq \frac{35}{5}$

Divide $x$ by $1$ .

$x \leq \frac{35}{5}$

Simplify the right side.

Divide $35$ by $5$ .

$x \leq 7$

Solve $5 x - 5 \geq - 25$ for $x$ .

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

Add $5$ to both sides of the inequality.

$5 x \geq - 25 + 5$

Add $- 25$ and $5$ .

$5 x \geq - 20$

Divide each term in $5 x \geq - 20$ by $5$ and simplify.

Divide each term in $5 x \geq - 20$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 20$ by $5$ .

$x \geq - 4$

Find the intersection of $x \leq 7$ and $x \geq - 4$ .

$- 4 \leq x \leq 7$

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x \leq 7$

Interval Notation:

$[- 4, 7]$

Solve the System of Inequalities 30>=5x-5>=-25

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