Algebra Examples

$- 5 \leq - 4 (2 x - 1) \leq 4$

Step 1

Apply the distributive property.

$- 5 \leq - 4 (2 x) - 4 \cdot - 1 \leq 4$

Step 2

Multiply.

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Step 2.1

Multiply $2$ by $- 4$ .

$- 5 \leq - 8 x - 4 \cdot - 1 \leq 4$

Step 2.2

Multiply $- 4$ by $- 1$ .

$- 5 \leq - 8 x + 4 \leq 4$

Step 3

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

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Step 3.1

Subtract $4$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 4 \leq - 8 x \leq 4 - 4$

Step 3.2

Subtract $4$ from $- 5$ .

$- 9 \leq - 8 x \leq 4 - 4$

Step 3.3

Subtract $4$ from $4$ .

$- 9 \leq - 8 x \leq 0$

Step 4

Divide each term in the inequality by $- 8$ .

$\frac{- 9}{- 8} \geq \frac{- 8 x}{- 8} \geq \frac{0}{- 8}$

Step 5

Dividing two negative values results in a positive value.

$\frac{9}{8} \geq \frac{- 8 x}{- 8} \geq \frac{0}{- 8}$

Step 6

Cancel the common factor of $- 8$ .

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Step 6.1

Cancel the common factor.

$\frac{9}{8} \geq \frac{- 8 x}{- 8} \geq \frac{0}{- 8}$

Step 6.2

Divide $x$ by $1$ .

$\frac{9}{8} \geq x \geq \frac{0}{- 8}$

Step 7

Divide $0$ by $- 8$ .

$\frac{9}{8} \geq x \geq 0$

Step 8

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

$0 \leq x \leq \frac{9}{8}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$0 \leq x \leq \frac{9}{8}$

Interval Notation:

$[0, \frac{9}{8}]$

Step 10