Algebra Examples

$22 \geq 4 m - 2$ or $5 - 3 m \leq - 13$

Step 1

Simplify the first inequality.

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Step 1.1

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

$4 m - 2 \leq 22$

Step 1.2

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

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Step 1.2.1

Add $2$ to both sides of the inequality.

$4 m \leq 22 + 2$

Step 1.2.2

Add $22$ and $2$ .

$4 m \leq 24$

Step 1.3

Divide each term in $4 m \leq 24$ by $4$ and simplify.

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Step 1.3.1

Divide each term in $4 m \leq 24$ by $4$ .

$\frac{4 m}{4} \leq \frac{24}{4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{4 m}{4} \leq \frac{24}{4}$

Step 1.3.2.1.2

Divide $m$ by $1$ .

$m \leq \frac{24}{4}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $24$ by $4$ .

$m \leq 6$

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Subtract $5$ from both sides of the inequality.

$- 3 m \leq - 13 - 5$

Step 2.1.2

Subtract $5$ from $- 13$ .

$- 3 m \leq - 18$

Step 2.2

Divide each term in $- 3 m \leq - 18$ by $- 3$ and simplify.

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Step 2.2.1

Divide each term in $- 3 m \leq - 18$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 m}{- 3} \geq \frac{- 18}{- 3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 3 m}{- 3} \geq \frac{- 18}{- 3}$

Step 2.2.2.1.2

Divide $m$ by $1$ .

$m \geq \frac{- 18}{- 3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 18$ by $- 3$ .

$m \geq 6$

Step 3

The union consists of all of the elements that are contained in each interval.

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Step 5