Algebra Examples

$a + 8 - 2 (a - 12) > 0$

Step 1

Simplify $a + 8 - 2 (a - 12)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$a + 8 - 2 a - 2 \cdot - 12 > 0$

Step 1.1.2

Multiply $- 2$ by $- 12$ .

$a + 8 - 2 a + 24 > 0$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $2 a$ from $a$ .

$- a + 8 + 24 > 0$

Step 1.2.2

Add $8$ and $24$ .

$- a + 32 > 0$

Step 2

Subtract $32$ from both sides of the inequality.

$- a > - 32$

Step 3

Divide each term in $- a > - 32$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- a > - 32$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- a}{- 1} < \frac{- 32}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} < \frac{- 32}{- 1}$

Step 3.2.2

Divide $a$ by $1$ .

$a < \frac{- 32}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 32$ by $- 1$ .

$a < 32$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a < 32$

Interval Notation:

$(- \infty, 32)$