Solve the inequality. Write the solution set in interval notation.
-$$( 2 y + 9 ) ( 4 y - 7 ) \leq 0$$
A) $\left( - \infty , - \frac { 9 } { 2 } \right) \cup \left( \frac { 7 } { 4 } , \infty \right)$
B) $\left( - \frac { 9 } { 2 } , \frac { 7 } { 4 } \right)$
C) $\left[ - \frac { 9 } { 2 } , \frac { 7 } { 4 } \right]$
D) $\left( - \infty , - \frac { 9 } { 2 } \right] \cup \left[ \frac { 7 } { 4 } , \infty \right)$

Question

Quizplus · Accepted Answer

The inequality $(2y + 9)(4y - 7) \leq 0$ is satisfied when either of the factors is zero or when one factor is positive and the other is negative. The roots of the equation are $y = -\frac{9}{2}$ and $y = \frac{7}{4}$. The inequality is satisfied between these two roots, including the endpoints, hence the correct interval notation is $\left[ - \frac { 9 } { 2 } , \frac { 7 } { 4 } \right]$.

Solve the Inequality (2y+9)(4y−7)≤0( 2 y + 9 ) ( 4 y - 7 ) \leq 0(2y+9)(4y−7)≤0

Solve the Inequality $( 2 y + 9 ) ( 4 y - 7 ) \leq 0$