Solve the System of Inequalities 2x+5<=-6 or 2x+5>=6

$2 x + 5 \leq - 6$ or $2 x + 5 \geq 6$

Step 1

Simplify the first inequality.

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

Subtract $5$ from both sides of the inequality.

$2 x \leq - 6 - 5$

Subtract $5$ from $- 6$ .

$2 x \leq - 11$

Divide each term in $2 x \leq - 11$ by $2$ and simplify.

Divide each term in $2 x \leq - 11$ by $2$ .

$\frac{2 x}{2} \leq \frac{- 11}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{- 11}{2}$

Divide $x$ by $1$ .

$x \leq \frac{- 11}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x \leq - \frac{11}{2}$

Step 2

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.

$2 x \geq 6 - 5$

Subtract $5$ from $6$ .

$2 x \geq 1$

Divide each term in $2 x \geq 1$ by $2$ and simplify.

Divide each term in $2 x \geq 1$ by $2$ .

$\frac{2 x}{2} \geq \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{1}{2}$

Divide $x$ by $1$ .

$x \geq \frac{1}{2}$

Step 3

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

$x \leq - \frac{11}{2}$ or $x \geq \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{11}{2} or x \geq \frac{1}{2}$

Interval Notation:

$(- \infty, - \frac{11}{2}] \cup [\frac{1}{2}, \infty)$

Step 5

Solve the System of Inequalities 2x+5<=-6 or 2x+5>=6

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