Question

Solve the inequality $x^2-8x+12<0$ algebraically.

Short answer

The solution for the inequality is $2<x<6$.

Step-by-step solution

Step 1. Write down the given inequality.

The given inequality is $x^2-8x+12<0$.

Step 2. Solve the given inequality.

Solving the inequality $x^2-8x+12<0$ by factoring it.

$\begin{array}{c}{x}^2-8x+12<\mathrm{0....}\left(\text{Given}\right)\\ \left(x-2\right)\left(x-6\right)<\mathrm{0....}\left(\text{Factoring}\right)\\ 2<x<6\\ x\in \left(2,6\right)\end{array}$

Step 3. Conclusion.

The solution for the inequality is $2<x<6$.