Question

Solve the inequality $15x^2+3x-12\le 0$ algebraically.

Short answer

The solution for the inequality is$x\in \left[-1,\frac{4}{5}\right]$.

Step-by-step solution

Step 1. Write down the given inequality.

The given inequality is $15x^2+3x-12\le 0$.

Step 2. Solve the given inequality.

Solving the inequality $15x^2+3x-12\le 0$ by factoring it.

$\begin{array}{c}15x^2+3x-12\le 0....\left(\text{Given}\right)\\ \left(x+1\right)\left(5x-4\right)\le 0....\left(\text{Factoring}\right)\\ -1\le x\le \frac{4}{5}\\ x\in \left[-1,\frac{4}{5}\right]\end{array}$

Step 3. Conclusion.

The solution for the inequality is $x\in \left[-1,\frac{4}{5}\right]$.