Algebra Examples

$4 (3 m + 10) \geq - 3 m - 51 + 8 m$

Step 1

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

$- 3 m - 51 + 8 m \leq 4 (3 m + 10)$

Step 2

Add $- 3 m$ and $8 m$ .

$5 m - 51 \leq 4 (3 m + 10)$

Step 3

Simplify $4 (3 m + 10)$ .

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Step 3.1

Apply the distributive property.

$5 m - 51 \leq 4 (3 m) + 4 \cdot 10$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $3$ by $4$ .

$5 m - 51 \leq 12 m + 4 \cdot 10$

Step 3.2.2

Multiply $4$ by $10$ .

$5 m - 51 \leq 12 m + 40$

Step 4

Move all terms containing $m$ to the left side of the inequality.

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Step 4.1

Subtract $12 m$ from both sides of the inequality.

$5 m - 51 - 12 m \leq 40$

Step 4.2

Subtract $12 m$ from $5 m$ .

$- 7 m - 51 \leq 40$

Step 5

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

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Step 5.1

Add $51$ to both sides of the inequality.

$- 7 m \leq 40 + 51$

Step 5.2

Add $40$ and $51$ .

$- 7 m \leq 91$

Step 6

Divide each term in $- 7 m \leq 91$ by $- 7$ and simplify.

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Step 6.1

Divide each term in $- 7 m \leq 91$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 m}{- 7} \geq \frac{91}{- 7}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 7$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 7 m}{- 7} \geq \frac{91}{- 7}$

Step 6.2.1.2

Divide $m$ by $1$ .

$m \geq \frac{91}{- 7}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $91$ by $- 7$ .

$m \geq - 13$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$m \geq - 13$

Interval Notation:

$[- 13, \infty)$