Algebra Examples

$- 3 < \frac{2 x - 6}{4} < 5$

Step 1

Cancel the common factor of $2 x - 6$ and $4$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$- 3 < \frac{2 (x) - 6}{4} < 5$

Step 1.2

Factor $2$ out of $- 6$ .

$- 3 < \frac{2 x + 2 \cdot - 3}{4} < 5$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot - 3$ .

$- 3 < \frac{2 (x - 3)}{4} < 5$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $4$ .

$- 3 < \frac{2 (x - 3)}{2 (2)} < 5$

Step 1.4.2

Cancel the common factor.

$- 3 < \frac{2 (x - 3)}{2 \cdot 2} < 5$

Step 1.4.3

Rewrite the expression.

$- 3 < \frac{x - 3}{2} < 5$

Step 2

Multiply each term in the inequality by $2$ .

$- 3 \cdot 2 < \frac{x - 3}{2} \cdot 2 < 5 \cdot 2$

Step 3

Multiply $- 3$ by $2$ .

$- 6 < \frac{x - 3}{2} \cdot 2 < 5 \cdot 2$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$- 6 < \frac{x - 3}{2} \cdot 2 < 5 \cdot 2$

Step 4.2

Rewrite the expression.

$- 6 < x - 3 < 5 \cdot 2$

Step 5

Multiply $5$ by $2$ .

$- 6 < x - 3 < 10$

Step 6

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

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Step 6.1

Add $3$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 + 3 < x < 10 + 3$

Step 6.2

Add $- 6$ and $3$ .

$- 3 < x < 10 + 3$

Step 6.3

Add $10$ and $3$ .

$- 3 < x < 13$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x < 13$

Interval Notation:

$(- 3, 13)$

Step 8