Solve for x 24<-2(x-3)<36

$24 < - 2 (x - 3) < 36$

Step 1

Apply the distributive property.

$24 < - 2 x - 2 \cdot - 3 < 36$

Step 2

Multiply $- 2$ by $- 3$ .

$24 < - 2 x + 6 < 36$

Step 3

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.

$24 - 6 < - 2 x < 36 - 6$

Subtract $6$ from $24$ .

$18 < - 2 x < 36 - 6$

Subtract $6$ from $36$ .

$18 < - 2 x < 30$

Step 4

Divide each term in the inequality by $- 2$ .

$\frac{18}{- 2} > \frac{- 2 x}{- 2} > \frac{30}{- 2}$

Step 5

Divide $18$ by $- 2$ .

$- 9 > \frac{- 2 x}{- 2} > \frac{30}{- 2}$

Step 6

Cancel the common factor of $- 2$ .

Cancel the common factor.

$- 9 > \frac{- 2 x}{- 2} > \frac{30}{- 2}$

Divide $x$ by $1$ .

$- 9 > x > \frac{30}{- 2}$

Step 7

Divide $30$ by $- 2$ .

$- 9 > x > - 15$

Step 8

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

$- 15 < x < - 9$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- 15 < x < - 9$

Interval Notation:

$(- 15, - 9)$

Step 10