Solve the System of Inequalities 3x-6<=24 or 30<=3x-6

$3 x - 6 \leq 24$ or $30 \leq 3 x - 6$

Step 1

Simplify the first inequality.

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

Add $6$ to both sides of the inequality.

$3 x \leq 24 + 6$

Add $24$ and $6$ .

$3 x \leq 30$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $30$ by $3$ .

$x \leq 10$

Step 2

Simplify the second inequality.

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

$3 x - 6 \geq 30$

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

Add $6$ to both sides of the inequality.

$3 x \geq 30 + 6$

Add $30$ and $6$ .

$3 x \geq 36$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $36$ by $3$ .

$x \geq 12$

Step 3

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

$x \leq 10$ or $x \geq 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 10 or x \geq 12$

Interval Notation:

$(- \infty, 10] \cup [12, \infty)$

Step 5

Solve the System of Inequalities 3x-6<=24 or 30<=3x-6

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