Graph 31>2x+7>27

$31 > 2 x + 7 > 27$

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.

$31 - 7 > 2 x > 27 - 7$

Subtract $7$ from $31$ .

$24 > 2 x > 27 - 7$

Subtract $7$ from $27$ .

$24 > 2 x > 20$

Divide each term in the inequality by $2$ .

$\frac{24}{2} > \frac{2 x}{2} > \frac{20}{2}$

Divide $24$ by $2$ .

$12 > \frac{2 x}{2} > \frac{20}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$12 > \frac{2 x}{2} > \frac{20}{2}$

Divide $x$ by $1$ .

$12 > x > \frac{20}{2}$

Divide $20$ by $2$ .

$12 > x > 10$

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

$10 < x < 12$