Solve for x -7<=11-x<7

$- 7 \leq 11 - x < 7$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Subtract $11$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 7 - 11 \leq - x < 7 - 11$

Subtract $11$ from $- 7$ .

$- 18 \leq - x < 7 - 11$

Subtract $11$ from $7$ .

$- 18 \leq - x < - 4$

Step 2

Multiply each term in the inequality by $- 1$ .

$\frac{- 18}{- 1} \geq \frac{- x}{- 1} > \frac{- 4}{- 1}$

Step 3

Divide $- 18$ by $- 1$ .

$18 \geq \frac{- x}{- 1} > \frac{- 4}{- 1}$

Step 4

Dividing two negative values results in a positive value.

$18 \geq \frac{x}{1} > \frac{- 4}{- 1}$

Step 5

Divide $x$ by $1$ .

$18 \geq x > \frac{- 4}{- 1}$

Step 6

Divide $- 4$ by $- 1$ .

$18 \geq x > 4$

Step 7

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$4 < x \leq 18$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$4 < x \leq 18$

Interval Notation:

$(4, 18]$

Step 9