Algebra Examples

$m + 9 < 8$ and $- 2 m \geq 10$

Step 1

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

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Step 1.1

Subtract $9$ from both sides of the inequality.

$m < 8 - 9$ and $- 2 m \geq 10$

Step 1.2

Subtract $9$ from $8$ .

$m < - 1$ and $- 2 m \geq 10$

Step 2

Divide each term in $- 2 m \geq 10$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 m \geq 10$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$m < - 1$ and $\frac{- 2 m}{- 2} \leq \frac{10}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$m < - 1$ and $\frac{- 2 m}{- 2} \leq \frac{10}{- 2}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m < - 1$ and $m \leq \frac{10}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $10$ by $- 2$ .

$m < - 1$ and $m \leq - 5$

Step 3

The intersection consists of the elements that are contained in both intervals.

$m \leq - 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m \leq - 5$

Interval Notation:

$(- \infty, - 5]$

Step 5