Questions: Put the steps in order to solve a quadratic inequality: First Get the inequality in standard form Factor Identify the critical points Express the solution Test the intervals Determine the solution Last

Solution Steps

To solve a quadratic inequality, follow these steps: First, get the inequality in standard form. Then, factor the quadratic expression. Identify the critical points by setting each factor equal to zero. Test the intervals determined by these critical points to see where the inequality holds true. Finally, express the solution based on the intervals that satisfy the inequality.

To solve a quadratic inequality, we need to follow a series of logical steps. Here is the correct order of steps with a brief summary of each:

First, ensure that the quadratic inequality is in the standard form, which is \( ax^2 + bx + c \leq 0 \), \( ax^2 + bx + c \geq 0 \), \( ax^2 + bx + c < 0 \), or \( ax^2 + bx + c > 0 \).

Next, factor the quadratic expression on one side of the inequality, if possible. This will help in identifying the critical points.

Determine the critical points by setting the factored expression equal to zero and solving for the variable. These points are where the expression changes sign.

Use the critical points to divide the number line into intervals. Test a point from each interval in the original inequality to determine whether the inequality holds in that interval.

Based on the test results, express the solution as a union of intervals where the inequality is satisfied.

Finally, write down the solution set, considering whether the inequality is strict (\(<\) or \(>\)) or inclusive (\(\leq\) or \(\geq\)).

Final Answer