Solve the System of Inequalities -x+10>=16 or 2>-x+10

$- x + 10 \geq 16$ or $2 > - x + 10$

Step 1

Simplify the first inequality.

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

Subtract $10$ from both sides of the inequality.

$- x \geq 16 - 10$ or $2 > - x + 10$

Subtract $10$ from $16$ .

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

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

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

$\frac{- x}{- 1} \leq \frac{6}{- 1}$ or $2 > - x + 10$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{6}{- 1}$ or $2 > - x + 10$

Divide $x$ by $1$ .

$x \leq \frac{6}{- 1}$ or $2 > - x + 10$

Simplify the right side.

Divide $6$ by $- 1$ .

$x \leq - 6$ or $2 > - x + 10$

Step 2

Simplify the second inequality.

Rewrite so $x$ is on the left side of the inequality.

$x \leq - 6$ or $- x + 10 < 2$

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

Subtract $10$ from both sides of the inequality.

$x \leq - 6$ or $- x < 2 - 10$

Subtract $10$ from $2$ .

$x \leq - 6$ or $- x < - 8$

Divide each term in $- x < - 8$ by $- 1$ and simplify.

Divide each term in $- x < - 8$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x \leq - 6$ or $\frac{- x}{- 1} > \frac{- 8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$x \leq - 6$ or $\frac{x}{1} > \frac{- 8}{- 1}$

Divide $x$ by $1$ .

$x \leq - 6$ or $x > \frac{- 8}{- 1}$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$x \leq - 6$ or $x > 8$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 6 or x > 8$

Interval Notation:

$(- \infty, - 6] \cup (8, \infty)$

Step 4

Solve the System of Inequalities -x+10>=16 or 2>-x+10

Related Questions

Support LCMGCF.com by disabling your adblocker.