Solve the System of Inequalities -4<(2x-3)/3<4

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

Solve $- 4 < \frac{2 x - 3}{3}$ for $x$ .

Multiply both sides by $3$ .

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

Simplify.

Simplify the left side.

Multiply $- 4$ by $3$ .

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

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$- 12 < 2 x - 3$

Solve for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$2 x - 3 > - 12$

Move all terms not containing $x$ to the right side of the inequality.

Add $3$ to both sides of the inequality.

$2 x > - 12 + 3$

Add $- 12$ and $3$ .

$2 x > - 9$

Divide each term in $2 x > - 9$ by $2$ and simplify.

Divide each term in $2 x > - 9$ by $2$ .

$\frac{2 x}{2} > \frac{- 9}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- 9}{2}$

Divide $x$ by $1$ .

$x > \frac{- 9}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{9}{2}$

Solve $\frac{2 x - 3}{3} < 4$ for $x$ .

Multiply both sides by $3$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$2 x - 3 < 4 \cdot 3$

Simplify the right side.

Multiply $4$ by $3$ .

$2 x - 3 < 12$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Add $3$ to both sides of the inequality.

$2 x < 12 + 3$

Add $12$ and $3$ .

$2 x < 15$

Divide each term in $2 x < 15$ by $2$ and simplify.

Divide each term in $2 x < 15$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Find the intersection of $x > - \frac{9}{2}$ and $x < \frac{15}{2}$ .

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

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 System of Inequalities -4<(2x-3)/3<4

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