Solve the System of Inequalities 5x+8<53 or 68<=5x+8

$5 x + 8 < 53$ or $68 \leq 5 x + 8$

Simplify the first inequality.

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

Subtract $8$ from both sides of the inequality.

$5 x < 53 - 8$ or $68 \leq 5 x + 8$

Subtract $8$ from $53$ .

$5 x < 45$ or $68 \leq 5 x + 8$

Divide each term in $5 x < 45$ by $5$ and simplify.

Divide each term in $5 x < 45$ by $5$ .

$\frac{5 x}{5} < \frac{45}{5}$ or $68 \leq 5 x + 8$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} < \frac{45}{5}$ or $68 \leq 5 x + 8$

Divide $x$ by $1$ .

$x < \frac{45}{5}$ or $68 \leq 5 x + 8$

Simplify the right side.

Divide $45$ by $5$ .

$x < 9$ or $68 \leq 5 x + 8$

Simplify the second inequality.

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

$x < 9$ or $5 x + 8 \geq 68$

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

Subtract $8$ from both sides of the inequality.

$x < 9$ or $5 x \geq 68 - 8$

Subtract $8$ from $68$ .

$x < 9$ or $5 x \geq 60$

Divide each term in $5 x \geq 60$ by $5$ and simplify.

Divide each term in $5 x \geq 60$ by $5$ .

$x < 9$ or $\frac{5 x}{5} \geq \frac{60}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$x < 9$ or $\frac{5 x}{5} \geq \frac{60}{5}$

Divide $x$ by $1$ .

$x < 9$ or $x \geq \frac{60}{5}$

Simplify the right side.

Divide $60$ by $5$ .

$x < 9$ or $x \geq 12$

The result can be shown in multiple forms.

Inequality Form:

$x < 9 or x \geq 12$

Interval Notation:

$(- \infty, 9) \cup [12, \infty)$