Algebra Examples

$- 5 \leq \frac{2 - 3 x}{4} \leq 9$

Step 1

Multiply each term in the inequality by $4$ .

$- 5 \cdot 4 \leq \frac{2 - 3 x}{4} \cdot 4 \leq 9 \cdot 4$

Step 2

Multiply $- 5$ by $4$ .

$- 20 \leq \frac{2 - 3 x}{4} \cdot 4 \leq 9 \cdot 4$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Cancel the common factor.

$- 20 \leq \frac{2 - 3 x}{4} \cdot 4 \leq 9 \cdot 4$

Step 3.2

Rewrite the expression.

$- 20 \leq 2 - 3 x \leq 9 \cdot 4$

Step 4

Multiply $9$ by $4$ .

$- 20 \leq 2 - 3 x \leq 36$

Step 5

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

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Step 5.1

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 20 - 2 \leq - 3 x \leq 36 - 2$

Step 5.2

Subtract $2$ from $- 20$ .

$- 22 \leq - 3 x \leq 36 - 2$

Step 5.3

Subtract $2$ from $36$ .

$- 22 \leq - 3 x \leq 34$

Step 6

Divide each term in the inequality by $- 3$ .

$\frac{- 22}{- 3} \geq \frac{- 3 x}{- 3} \geq \frac{34}{- 3}$

Step 7

Dividing two negative values results in a positive value.

$\frac{22}{3} \geq \frac{- 3 x}{- 3} \geq \frac{34}{- 3}$

Step 8

Cancel the common factor of $- 3$ .

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Step 8.1

Cancel the common factor.

$\frac{22}{3} \geq \frac{- 3 x}{- 3} \geq \frac{34}{- 3}$

Step 8.2

Divide $x$ by $1$ .

$\frac{22}{3} \geq x \geq \frac{34}{- 3}$

Step 9

Move the negative in front of the fraction.

$\frac{22}{3} \geq x \geq - \frac{34}{3}$

Step 10

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- \frac{34}{3} \leq x \leq \frac{22}{3}$

Step 11

The result can be shown in multiple forms.

Inequality Form:

$- \frac{34}{3} \leq x \leq \frac{22}{3}$

Interval Notation:

$[- \frac{34}{3}, \frac{22}{3}]$

Step 12