Solve the inequality. Write the answer in interval notation. $$- 2

Question

Solve the inequality. Write the answer in interval notation. $$- 2 < - 2 y + 19 < 10$$
A) $\left[ \frac { 9 } { 2 } , \frac { 21 } { 2 } \right]$
B) $\left( \frac { 9 } { 2 } , \frac { 21 } { 2 } \right)$
C) $\left( \frac { 21 } { 2 } , 10 \right)$
D) $\left( \frac { 21 } { 2 } , \frac { 9 } { 2 } \right)$

Quizplus · Accepted Answer

First, add 2 to all parts of the inequality to get $0 < -2y + 21 < 12$. Then, subtract 21 from all parts to get $-21 < -2y < -9$. Divide all parts by -2 (and flip the inequality signs because of dividing by a negative) to get $\frac{9}{2} < y < \frac{21}{2}$. This corresponds to option B in interval notation, which uses parentheses to indicate that the endpoints are not included in the interval.

Solve the Inequality −2<−2y+19<10- 2 < - 2 y + 19 < 10−2<−2y+19<10

Solve the Inequality $- 2 < - 2 y + 19 < 10$