Solve the Inequality for x -4<(6x-9)/9<4

$- 4 < \frac{6 x - 9}{9} < 4$

Cancel the common factor of $6 x - 9$ and $9$ .

Factor $3$ out of $6 x$ .

$- 4 < \frac{3 (2 x) - 9}{9} < 4$

Factor $3$ out of $- 9$ .

$- 4 < \frac{3 (2 x) + 3 (- 3)}{9} < 4$

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

$- 4 < \frac{3 (2 x - 3)}{9} < 4$

Cancel the common factors.

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply each term in the inequality by $3$ .

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

Multiply $- 4$ by $3$ .

$- 12 < \frac{2 x - 3}{3} \cdot 3 < 4 \cdot 3$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 12 < \frac{2 x - 3}{3} \cdot 3 < 4 \cdot 3$

Rewrite the expression.

$- 12 < 2 x - 3 < 4 \cdot 3$

Multiply $4$ by $3$ .

$- 12 < 2 x - 3 < 12$

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

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

$- 12 + 3 < 2 x < 12 + 3$

Add $- 12$ and $3$ .

$- 9 < 2 x < 12 + 3$

Add $12$ and $3$ .

$- 9 < 2 x < 15$

Divide each term in the inequality by $2$ .

$\frac{- 9}{2} < \frac{2 x}{2} < \frac{15}{2}$

Move the negative in front of the fraction.

$- \frac{9}{2} < \frac{2 x}{2} < \frac{15}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{9}{2} < \frac{2 x}{2} < \frac{15}{2}$

Divide $x$ by $1$ .

$- \frac{9}{2} < x < \frac{15}{2}$

The result can be shown in multiple forms.

Inequality Form:

$- \frac{9}{2} < x < \frac{15}{2}$

Interval Notation:

$(- \frac{9}{2}, \frac{15}{2})$

Solve the Inequality for x -4<(6x-9)/9<4

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