Solve the Inequality for x -16<x/-4+6<=-2

$- 16 < \frac{x}{- 4} + 6 \leq - 2$

Move the negative in front of the fraction.

$- 16 < - \frac{x}{4} + 6 \leq - 2$

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

Subtract $6$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 16 - 6 < - \frac{x}{4} \leq - 2 - 6$

Subtract $6$ from $- 16$ .

$- 22 < - \frac{x}{4} \leq - 2 - 6$

Multiply each term in the inequality by $4$ .

$- 22 \cdot 4 < - \frac{x}{4} \cdot 4 \leq - 2 \cdot 4 - 6 \cdot 4$

Multiply $- 22$ by $4$ .

$- 88 < - \frac{x}{4} \cdot 4 \leq - 2 \cdot 4 - 6 \cdot 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$- 88 < \frac{- x}{4} \cdot 4 \leq - 2 \cdot 4 - 6 \cdot 4$

Cancel the common factor.

$- 88 < \frac{- x}{4} \cdot 4 \leq - 2 \cdot 4 - 6 \cdot 4$

Rewrite the expression.

$- 88 < - x \leq - 2 \cdot 4 - 6 \cdot 4$

Simplify each term.

Multiply $- 2$ by $4$ .

$- 88 < - x \leq - 8 - 6 \cdot 4$

Multiply $- 6$ by $4$ .

$- 88 < - x \leq - 8 - 24$

Subtract $24$ from $- 8$ .

$- 88 < - x \leq - 32$

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

$\frac{- 88}{- 1} > \frac{- x}{- 1} \geq \frac{- 32}{- 1}$

Divide $- 88$ by $- 1$ .

$88 > \frac{- x}{- 1} \geq \frac{- 32}{- 1}$

Dividing two negative values results in a positive value.

$88 > \frac{x}{1} \geq \frac{- 32}{- 1}$

Divide $x$ by $1$ .

$88 > x \geq \frac{- 32}{- 1}$

Divide $- 32$ by $- 1$ .

$88 > x \geq 32$

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

$32 \leq x < 88$

The result can be shown in multiple forms.

Inequality Form:

$32 \leq x < 88$

Interval Notation:

$[32, 88)$