Solve the System of Inequalities 5x-4>=12 or 12x+5<=-4

$5 x - 4 \geq 12$ or $12 x + 5 \leq - 4$

Simplify the first inequality.

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

Add $4$ to both sides of the inequality.

$5 x \geq 12 + 4$

Add $12$ and $4$ .

$5 x \geq 16$

Divide each term in $5 x \geq 16$ by $5$ and simplify.

Divide each term in $5 x \geq 16$ by $5$ .

$\frac{5 x}{5} \geq \frac{16}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{16}{5}$

Divide $x$ by $1$ .

$x \geq \frac{16}{5}$

Simplify the second inequality.

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

Subtract $5$ from both sides of the inequality.

$12 x \leq - 4 - 5$

Subtract $5$ from $- 4$ .

$12 x \leq - 9$

Divide each term in $12 x \leq - 9$ by $12$ and simplify.

Divide each term in $12 x \leq - 9$ by $12$ .

$\frac{12 x}{12} \leq \frac{- 9}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} \leq \frac{- 9}{12}$

Divide $x$ by $1$ .

$x \leq \frac{- 9}{12}$

Simplify the right side.

Cancel the common factor of $- 9$ and $12$ .

Factor $3$ out of $- 9$ .

$x \leq \frac{3 (- 3)}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

$x \leq \frac{3 \cdot - 3}{3 \cdot 4}$

Cancel the common factor.

$x \leq \frac{3 \cdot - 3}{3 \cdot 4}$

Rewrite the expression.

$x \leq \frac{- 3}{4}$

Move the negative in front of the fraction.

$x \leq - \frac{3}{4}$

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

$x \leq - \frac{3}{4}$ or $x \geq \frac{16}{5}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{3}{4} or x \geq \frac{16}{5}$

Interval Notation:

$(- \infty, - \frac{3}{4}] \cup [\frac{16}{5}, \infty)$

Solve the System of Inequalities 5x-4>=12 or 12x+5<=-4

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