Solve the System of Inequalities 2x-5>-11 or -10x-6>=44

$2 x - 5 > - 11$ or $- 10 x - 6 \geq 44$

Step 1

Simplify the first inequality.

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

Add $5$ to both sides of the inequality.

$2 x > - 11 + 5$ or $- 10 x - 6 \geq 44$

Add $- 11$ and $5$ .

$2 x > - 6$ or $- 10 x - 6 \geq 44$

Divide each term in $2 x > - 6$ by $2$ and simplify.

Divide each term in $2 x > - 6$ by $2$ .

$\frac{2 x}{2} > \frac{- 6}{2}$ or $- 10 x - 6 \geq 44$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- 6}{2}$ or $- 10 x - 6 \geq 44$

Divide $x$ by $1$ .

$x > \frac{- 6}{2}$ or $- 10 x - 6 \geq 44$

Simplify the right side.

Divide $- 6$ by $2$ .

$x > - 3$ or $- 10 x - 6 \geq 44$

Step 2

Simplify the second inequality.

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

Add $6$ to both sides of the inequality.

$x > - 3$ or $- 10 x \geq 44 + 6$

Add $44$ and $6$ .

$x > - 3$ or $- 10 x \geq 50$

Divide each term in $- 10 x \geq 50$ by $- 10$ and simplify.

Divide each term in $- 10 x \geq 50$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x > - 3$ or $\frac{- 10 x}{- 10} \leq \frac{50}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$x > - 3$ or $\frac{- 10 x}{- 10} \leq \frac{50}{- 10}$

Divide $x$ by $1$ .

$x > - 3$ or $x \leq \frac{50}{- 10}$

Simplify the right side.

Divide $50$ by $- 10$ .

$x > - 3$ or $x \leq - 5$

Step 3

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

$x \leq - 5$ or $x > - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 5 or x > - 3$

Interval Notation:

$(- \infty, - 5] \cup (- 3, \infty)$

Step 5

Solve the System of Inequalities 2x-5>-11 or -10x-6>=44

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