Solve the inequality.
-$( 2 x - 3 ) \sqrt { x + 1 }

Question

Solve the inequality.
-$( 2 x - 3 ) \sqrt { x + 1 } < 0$
A) $[ 3 / 2,1 ]$
B) $( - 1,3 / 2 )$
C) $( 3 / 2 , \infty )$
D) $( \infty , 3 / 2 )$

Quizplus · Accepted Answer

For the inequality $(2x - 3)\sqrt{x + 1} < 0$ to hold, we must consider the sign of each factor separately. The square root $\sqrt{x + 1}$ is non-negative for $x \geq -1$ and undefined for $x < -1$. The linear expression $2x - 3$ is negative for $x < \frac{3}{2}$ and positive for $x > \frac{3}{2}$. The inequality is satisfied when $2x - 3 < 0$ and $\sqrt{x + 1} \geq 0$, which occurs for $-1 \leq x < \frac{3}{2}$. Therefore, the solution set is $(-1, \frac{3}{2})$.

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