Solve the Inequality for x -1/2<(2x-13)/12<=2/3

$- \frac{1}{2} < \frac{2 x - 13}{12} \leq \frac{2}{3}$

Multiply each term in the inequality by $12$ .

$- \frac{1}{2} \cdot 12 < \frac{2 x - 13}{12} \cdot 12 \leq \frac{2}{3} \cdot 12$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} \cdot 12 < \frac{2 x - 13}{12} \cdot 12 \leq \frac{2}{3} \cdot 12$

Factor $2$ out of $12$ .

$\frac{- 1}{2} \cdot (2 (6)) < \frac{2 x - 13}{12} \cdot 12 \leq \frac{2}{3} \cdot 12$

Cancel the common factor.

$\frac{- 1}{2} \cdot (2 \cdot 6) < \frac{2 x - 13}{12} \cdot 12 \leq \frac{2}{3} \cdot 12$

Rewrite the expression.

$- 1 \cdot 6 < \frac{2 x - 13}{12} \cdot 12 \leq \frac{2}{3} \cdot 12$

Multiply $- 1$ by $6$ .

$- 6 < \frac{2 x - 13}{12} \cdot 12 \leq \frac{2}{3} \cdot 12$

Cancel the common factor of $12$ .

Cancel the common factor.

$- 6 < \frac{2 x - 13}{12} \cdot 12 \leq \frac{2}{3} \cdot 12$

Rewrite the expression.

$- 6 < 2 x - 13 \leq \frac{2}{3} \cdot 12$

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$- 6 < 2 x - 13 \leq \frac{2}{3} \cdot (3 (4))$

Cancel the common factor.

$- 6 < 2 x - 13 \leq \frac{2}{3} \cdot (3 \cdot 4)$

Rewrite the expression.

$- 6 < 2 x - 13 \leq 2 \cdot 4$

Multiply $2$ by $4$ .

$- 6 < 2 x - 13 \leq 8$

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

Add $13$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 + 13 < 2 x \leq 8 + 13$

Add $- 6$ and $13$ .

$7 < 2 x \leq 8 + 13$

Add $8$ and $13$ .

$7 < 2 x \leq 21$

Divide each term in the inequality by $2$ .

$\frac{7}{2} < \frac{2 x}{2} \leq \frac{21}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7}{2} < \frac{2 x}{2} \leq \frac{21}{2}$

Divide $x$ by $1$ .

$\frac{7}{2} < x \leq \frac{21}{2}$

The result can be shown in multiple forms.

Inequality Form:

$\frac{7}{2} < x \leq \frac{21}{2}$

Interval Notation:

$(\frac{7}{2}, \frac{21}{2}]$

Solve the Inequality for x -1/2<(2x-13)/12<=2/3

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