Algebra Examples

$- 5 \leq 2 (4 x + 3) \leq 10$

Step 1

Apply the distributive property.

$- 5 \leq 2 (4 x) + 2 \cdot 3 \leq 10$

Step 2

Multiply.

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Step 2.1

Multiply $4$ by $2$ .

$- 5 \leq 8 x + 2 \cdot 3 \leq 10$

Step 2.2

Multiply $2$ by $3$ .

$- 5 \leq 8 x + 6 \leq 10$

Step 3

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

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Step 3.1

Subtract $6$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 6 \leq 8 x \leq 10 - 6$

Step 3.2

Subtract $6$ from $- 5$ .

$- 11 \leq 8 x \leq 10 - 6$

Step 3.3

Subtract $6$ from $10$ .

$- 11 \leq 8 x \leq 4$

Step 4

Divide each term in the inequality by $8$ .

$\frac{- 11}{8} \leq \frac{8 x}{8} \leq \frac{4}{8}$

Step 5

Move the negative in front of the fraction.

$- \frac{11}{8} \leq \frac{8 x}{8} \leq \frac{4}{8}$

Step 6

Cancel the common factor of $8$ .

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Step 6.1

Cancel the common factor.

$- \frac{11}{8} \leq \frac{8 x}{8} \leq \frac{4}{8}$

Step 6.2

Divide $x$ by $1$ .

$- \frac{11}{8} \leq x \leq \frac{4}{8}$

Step 7

Cancel the common factor of $4$ and $8$ .

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Step 7.1

Factor $4$ out of $4$ .

$- \frac{11}{8} \leq x \leq \frac{4 (1)}{8}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $4$ out of $8$ .

$- \frac{11}{8} \leq x \leq \frac{4 \cdot 1}{4 \cdot 2}$

Step 7.2.2

Cancel the common factor.

$- \frac{11}{8} \leq x \leq \frac{4 \cdot 1}{4 \cdot 2}$

Step 7.2.3

Rewrite the expression.

$- \frac{11}{8} \leq x \leq \frac{1}{2}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$- \frac{11}{8} \leq x \leq \frac{1}{2}$

Interval Notation:

$[- \frac{11}{8}, \frac{1}{2}]$

Step 9