Solve the Inequality for x -x-4<=x-12<=-x+2

$- x - 4 \leq x - 12 \leq - x + 2$

Step 1

Solve $- x - 4 \leq x - 12$ for $x$ .

Move all terms containing $x$ to the left side of the inequality.

Subtract $x$ from both sides of the inequality.

$- x - 4 - x \leq - 12$

Subtract $x$ from $- x$ .

$- 2 x - 4 \leq - 12$

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

Add $4$ to both sides of the inequality.

$- 2 x \leq - 12 + 4$

Add $- 12$ and $4$ .

$- 2 x \leq - 8$

Divide each term in $- 2 x \leq - 8$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq - 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{- 8}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$x \geq 4$

Step 2

Solve $x - 12 \leq - x + 2$ for $x$ .

Move all terms containing $x$ to the left side of the inequality.

Add $x$ to both sides of the inequality.

$x - 12 + x \leq 2$

Add $x$ and $x$ .

$2 x - 12 \leq 2$

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

Add $12$ to both sides of the inequality.

$2 x \leq 2 + 12$

Add $2$ and $12$ .

$2 x \leq 14$

Divide each term in $2 x \leq 14$ by $2$ and simplify.

Divide each term in $2 x \leq 14$ by $2$ .

$\frac{2 x}{2} \leq \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{14}{2}$

Divide $x$ by $1$ .

$x \leq \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x \leq 7$

Step 3

Find the intersection of $x \geq 4$ and $x \leq 7$ .

$4 \leq x \leq 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$4 \leq x \leq 7$

Interval Notation:

$[4, 7]$

Step 5

Solve the Inequality for x -x-4<=x-12<=-x+2

Related Questions

Support LCMGCF.com by disabling your adblocker.