Algebra Examples

$- 57 \leq 3 (3 x - 4) < 24$

Step 1

Apply the distributive property.

$- 57 \leq 3 (3 x) + 3 \cdot - 4 < 24$

Step 2

Multiply.

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Step 2.1

Multiply $3$ by $3$ .

$- 57 \leq 9 x + 3 \cdot - 4 < 24$

Step 2.2

Multiply $3$ by $- 4$ .

$- 57 \leq 9 x - 12 < 24$

Step 3

Move all terms not containing $x$ from the center section of the inequality.

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Step 3.1

Add $12$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 57 + 12 \leq 9 x < 24 + 12$

Step 3.2

Add $- 57$ and $12$ .

$- 45 \leq 9 x < 24 + 12$

Step 3.3

Add $24$ and $12$ .

$- 45 \leq 9 x < 36$

Step 4

Divide each term in the inequality by $9$ .

$\frac{- 45}{9} \leq \frac{9 x}{9} < \frac{36}{9}$

Step 5

Divide $- 45$ by $9$ .

$- 5 \leq \frac{9 x}{9} < \frac{36}{9}$

Step 6

Cancel the common factor of $9$ .

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Step 6.1

Cancel the common factor.

$- 5 \leq \frac{9 x}{9} < \frac{36}{9}$

Step 6.2

Divide $x$ by $1$ .

$- 5 \leq x < \frac{36}{9}$

Step 7

Divide $36$ by $9$ .

$- 5 \leq x < 4$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$- 5 \leq x < 4$

Interval Notation:

$[- 5, 4)$

Step 9