Solve the System of Inequalities 32>3x-4>-34

$32 > 3 x - 4 > - 34$

Step 1

Solve $32 > 3 x - 4$ for $x$ .

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

$3 x - 4 < 32$

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

Add $4$ to both sides of the inequality.

$3 x < 32 + 4$

Add $32$ and $4$ .

$3 x < 36$

Divide each term in $3 x < 36$ by $3$ and simplify.

Divide each term in $3 x < 36$ by $3$ .

$\frac{3 x}{3} < \frac{36}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{36}{3}$

Divide $x$ by $1$ .

$x < \frac{36}{3}$

Simplify the right side.

Divide $36$ by $3$ .

$x < 12$

Step 2

Solve $3 x - 4 > - 34$ for $x$ .

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

Add $4$ to both sides of the inequality.

$3 x > - 34 + 4$

Add $- 34$ and $4$ .

$3 x > - 30$

Divide each term in $3 x > - 30$ by $3$ and simplify.

Divide each term in $3 x > - 30$ by $3$ .

$\frac{3 x}{3} > \frac{- 30}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{- 30}{3}$

Divide $x$ by $1$ .

$x > \frac{- 30}{3}$

Simplify the right side.

Divide $- 30$ by $3$ .

$x > - 10$

Step 3

Find the intersection of $x < 12$ and $x > - 10$ .

$- 10 < x < 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 10 < x < 12$

Interval Notation:

$(- 10, 12)$

Step 5

Solve the System of Inequalities 32>3x-4>-34

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