Solve the System of Inequalities 32<=3x+2 or 38>=3x+2

$32 \leq 3 x + 2$ or $38 \geq 3 x + 2$

Step 1

Simplify the first inequality.

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

$3 x + 2 \geq 32$

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

Subtract $2$ from both sides of the inequality.

$3 x \geq 32 - 2$

Subtract $2$ from $32$ .

$3 x \geq 30$

Divide each term in $3 x \geq 30$ by $3$ and simplify.

Divide each term in $3 x \geq 30$ by $3$ .

$\frac{3 x}{3} \geq \frac{30}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{30}{3}$

Divide $x$ by $1$ .

$x \geq \frac{30}{3}$

Simplify the right side.

Divide $30$ by $3$ .

$x \geq 10$

Step 2

Simplify the second inequality.

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

$3 x + 2 \leq 38$

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

Subtract $2$ from both sides of the inequality.

$3 x \leq 38 - 2$

Subtract $2$ from $38$ .

$3 x \leq 36$

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

Divide each term in $3 x \leq 36$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $36$ by $3$ .

$x \leq 12$

Step 3

The union consists of all of the elements that are contained in each interval.

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Step 5

Solve the System of Inequalities 32<=3x+2 or 38>=3x+2

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