Solve the System of Inequalities -x+6<12 or -x+6>2

$- x + 6 < 12$ or $- x + 6 > 2$

Step 1

Simplify the first inequality.

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

Subtract $6$ from both sides of the inequality.

$- x < 12 - 6$ or $- x + 6 > 2$

Subtract $6$ from $12$ .

$- x < 6$ or $- x + 6 > 2$

Divide each term in $- x < 6$ by $- 1$ and simplify.

Divide each term in $- x < 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{6}{- 1}$ or $- x + 6 > 2$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{6}{- 1}$ or $- x + 6 > 2$

Divide $x$ by $1$ .

$x > \frac{6}{- 1}$ or $- x + 6 > 2$

Simplify the right side.

Divide $6$ by $- 1$ .

$x > - 6$ or $- x + 6 > 2$

Step 2

Simplify the second inequality.

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

Subtract $6$ from both sides of the inequality.

$x > - 6$ or $- x > 2 - 6$

Subtract $6$ from $2$ .

$x > - 6$ or $- x > - 4$

Divide each term in $- x > - 4$ by $- 1$ and simplify.

Divide each term in $- x > - 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x > - 6$ or $\frac{- x}{- 1} < \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$x > - 6$ or $\frac{x}{1} < \frac{- 4}{- 1}$

Divide $x$ by $1$ .

$x > - 6$ or $x < \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$x > - 6$ or $x < 4$

Step 3

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

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Step 5

Solve the System of Inequalities -x+6<12 or -x+6>2

Related Questions

Support LCMGCF.com by disabling your adblocker.