Solve the System of Inequalities 5x-4<=-29 or 5x-4>=16

$5 x - 4 \leq - 29$ or $5 x - 4 \geq 16$

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.

$5 x \leq - 29 + 4$

Add $- 29$ and $4$ .

$5 x \leq - 25$

Divide each term in $5 x \leq - 25$ by $5$ and simplify.

Divide each term in $5 x \leq - 25$ by $5$ .

$\frac{5 x}{5} \leq \frac{- 25}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \leq \frac{- 25}{5}$

Divide $x$ by $1$ .

$x \leq \frac{- 25}{5}$

Simplify the right side.

Divide $- 25$ by $5$ .

$x \leq - 5$

Simplify the second inequality.

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

Add $4$ to both sides of the inequality.

$5 x \geq 16 + 4$

Add $16$ and $4$ .

$5 x \geq 20$

Divide each term in $5 x \geq 20$ by $5$ and simplify.

Divide each term in $5 x \geq 20$ by $5$ .

$\frac{5 x}{5} \geq \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{20}{5}$

Divide $x$ by $1$ .

$x \geq \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x \geq 4$

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

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

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \infty, - 5] \cup [4, \infty)$