Pre-Algebra Examples

$- 2 \leq 2 (x - 4) \leq 6$

Step 1

Apply the distributive property.

$- 2 \leq 2 x + 2 \cdot - 4 \leq 6$

Step 2

Multiply $2$ by $- 4$ .

$- 2 \leq 2 x - 8 \leq 6$

Step 3

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

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Step 3.1

Add $8$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 2 + 8 \leq 2 x \leq 6 + 8$

Step 3.2

Add $- 2$ and $8$ .

$6 \leq 2 x \leq 6 + 8$

Step 3.3

Add $6$ and $8$ .

$6 \leq 2 x \leq 14$

Step 4

Divide each term in the inequality by $2$ .

$\frac{6}{2} \leq \frac{2 x}{2} \leq \frac{14}{2}$

Step 5

Divide $6$ by $2$ .

$3 \leq \frac{2 x}{2} \leq \frac{14}{2}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Cancel the common factor.

$3 \leq \frac{2 x}{2} \leq \frac{14}{2}$

Step 6.2

Divide $x$ by $1$ .

$3 \leq x \leq \frac{14}{2}$

Step 7

Divide $14$ by $2$ .

$3 \leq x \leq 7$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$3 \leq x \leq 7$

Interval Notation:

$[3, 7]$

Step 9