Solve for x -1<=7-4x<15

$- 1 \leq 7 - 4 x < 15$

Step 1

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

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

$- 1 - 7 \leq - 4 x < 15 - 7$

Subtract $7$ from $- 1$ .

$- 8 \leq - 4 x < 15 - 7$

Subtract $7$ from $15$ .

$- 8 \leq - 4 x < 8$

Step 2

Divide each term in the inequality by $- 4$ .

$\frac{- 8}{- 4} \geq \frac{- 4 x}{- 4} > \frac{8}{- 4}$

Step 3

Divide $- 8$ by $- 4$ .

$2 \geq \frac{- 4 x}{- 4} > \frac{8}{- 4}$

Step 4

Cancel the common factor of $- 4$ .

Cancel the common factor.

$2 \geq \frac{- 4 x}{- 4} > \frac{8}{- 4}$

Divide $x$ by $1$ .

$2 \geq x > \frac{8}{- 4}$

Step 5

Divide $8$ by $- 4$ .

$2 \geq x > - 2$

Step 6

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

$- 2 < x \leq 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x \leq 2$

Interval Notation:

$(- 2, 2]$

Step 8