Algebra Examples

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

Step 1

Cancel the common factor of $6 x - 3$ and $3$ .

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Step 1.1

Factor $3$ out of $6 x$ .

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

Step 1.2

Factor $3$ out of $- 3$ .

$- 5 < \frac{3 (2 x) + 3 \cdot - 1}{3} < 5$

Step 1.3

Factor $3$ out of $3 (2 x) + 3 (- 1)$ .

$- 5 < \frac{3 (2 x - 1)}{3} < 5$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $3$ .

$- 5 < \frac{3 (2 x - 1)}{3 (1)} < 5$

Step 1.4.2

Cancel the common factor.

$- 5 < \frac{3 (2 x - 1)}{3 \cdot 1} < 5$

Step 1.4.3

Rewrite the expression.

$- 5 < \frac{2 x - 1}{1} < 5$

Step 1.4.4

Divide $2 x - 1$ by $1$ .

$- 5 < 2 x - 1 < 5$

Step 2

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

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Step 2.1

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 + 1 < 2 x < 5 + 1$

Step 2.2

Add $- 5$ and $1$ .

$- 4 < 2 x < 5 + 1$

Step 2.3

Add $5$ and $1$ .

$- 4 < 2 x < 6$

Step 3

Divide each term in the inequality by $2$ .

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

Step 4

Divide $- 4$ by $2$ .

$- 2 < \frac{2 x}{2} < \frac{6}{2}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$- 2 < \frac{2 x}{2} < \frac{6}{2}$

Step 5.2

Divide $x$ by $1$ .

$- 2 < x < \frac{6}{2}$

Step 6

Divide $6$ by $2$ .

$- 2 < x < 3$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x < 3$

Interval Notation:

$(- 2, 3)$

Step 8