Solve for x -8<-(x+7)<=3

$- 8 < - (x + 7) \leq 3$

Step 1

Apply the distributive property.

$- 8 < - x - 1 \cdot 7 \leq 3$

Step 2

Multiply $- 1$ by $7$ .

$- 8 < - x - 7 \leq 3$

Step 3

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

Add $7$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 8 + 7 < - x \leq 3 + 7$

Add $- 8$ and $7$ .

$- 1 < - x \leq 3 + 7$

Add $3$ and $7$ .

$- 1 < - x \leq 10$

Step 4

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

$\frac{- 1}{- 1} > \frac{- x}{- 1} \geq \frac{10}{- 1}$

Step 5

Divide $- 1$ by $- 1$ .

$1 > \frac{- x}{- 1} \geq \frac{10}{- 1}$

Step 6

Dividing two negative values results in a positive value.

$1 > \frac{x}{1} \geq \frac{10}{- 1}$

Step 7

Divide $x$ by $1$ .

$1 > x \geq \frac{10}{- 1}$

Step 8

Divide $10$ by $- 1$ .

$1 > x \geq - 10$

Step 9

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

$- 10 \leq x < 1$

Step 10

The result can be shown in multiple forms.

Inequality Form:

$- 10 \leq x < 1$

Interval Notation:

$[- 10, 1)$

Step 11