Question

Solve the inequality $x^2+2x-86\ge -23$ algebraically.

Short answer

The solution for the inequality is$x\in \left(-\infty ,-9\right)\cup \left(7,\infty \right)$.

Step-by-step solution

Step 1. Write down the given inequality.

The given inequality is $x^2+2x-86\ge -23$.

Step 2. Solve the given inequality.

Solving the inequality $x^2+2x-86\ge -23$ by factoring it.

$\begin{array}{c}{x}^2+2x-86\ge -23....\left(\text{Given}\right)\\ x^2+2x-63\ge 0\\ \left(x+9\right)\left(x-7\right)\ge 0....\left(\text{Factoring}\right)\\ x\le -9\text{or}x\ge 7\\ x\in \left(-\infty ,-9\right)\cup \left(7,\infty \right)\end{array}$

Step 3. Conclusion.

The solution for the inequality is $x\in \left(-\infty ,-9\right)\cup \left(7,\infty \right)$.