Algebra Examples

$- 60 \leq - 5 x - 10$ or $- 5 x - 10 \geq - 70$

Step 1

Simplify the first inequality.

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Step 1.1

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

$- 5 x - 10 \geq - 60$

Step 1.2

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

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Step 1.2.1

Add $10$ to both sides of the inequality.

$- 5 x \geq - 60 + 10$

Step 1.2.2

Add $- 60$ and $10$ .

$- 5 x \geq - 50$

Step 1.3

Divide each term in $- 5 x \geq - 50$ by $- 5$ and simplify.

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Step 1.3.1

Divide each term in $- 5 x \geq - 50$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{- 50}{- 5}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{- 50}{- 5}$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 50}{- 5}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $- 50$ by $- 5$ .

$x \leq 10$

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Add $10$ to both sides of the inequality.

$- 5 x \geq - 70 + 10$

Step 2.1.2

Add $- 70$ and $10$ .

$- 5 x \geq - 60$

Step 2.2

Divide each term in $- 5 x \geq - 60$ by $- 5$ and simplify.

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Step 2.2.1

Divide each term in $- 5 x \geq - 60$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{- 60}{- 5}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 5$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{- 60}{- 5}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 60}{- 5}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 60$ by $- 5$ .

$x \leq 12$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq 12$

Interval Notation:

$(- \infty, 12]$

Step 4