Algebra Examples

11 a - 4 (a + 2) \leq 8 a + 10

$11 a - 4 (a + 2) \leq 8 a + 10$

Step 1

Simplify

$11 a - 4 (a + 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$11 a - 4 a - 4 \cdot 2 \leq 8 a + 10$

Step 1.1.2

Multiply

$- 4$ by

$2$ .

$11 a - 4 a - 8 \leq 8 a + 10$

Step 1.2

Subtract

$4 a$ from

$11 a$ .

$7 a - 8 \leq 8 a + 10$

Step 2

Move all terms containing

$a$ to the left side of the inequality.

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Step 2.1

Subtract

$8 a$ from both sides of the inequality.

$7 a - 8 - 8 a \leq 10$

Step 2.2

Subtract

$8 a$ from

$7 a$ .

$- a - 8 \leq 10$

Step 3

Move all terms not containing

$a$ to the right side of the inequality.

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Step 3.1

Add

$8$ to both sides of the inequality.

$- a \leq 10 + 8$

Step 3.2

Add

$10$ and

$8$ .

$- a \leq 18$

Step 4

Divide each term in

$- a \leq 18$ by

$- 1$ and simplify.

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Step 4.1

Divide each term in

$- a \leq 18$ by

$- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- a}{- 1} \geq \frac{18}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} \geq \frac{18}{- 1}$

Step 4.2.2

Divide

$a$ by

$1$ .

$a \geq \frac{18}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide

$18$ by

$- 1$ .

$a \geq - 18$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$a \geq - 18$

Interval Notation:

$[- 18, \infty)$