Question
Studdy Solution
STEP 1
1. The inequality is a quadratic inequality.
2. Solving the inequality involves finding the roots of the corresponding quadratic equation and determining the intervals where the inequality holds.
STEP 2
1. Find the roots of the quadratic equation .
2. Determine the intervals defined by the roots.
3. Test the intervals to find where the inequality holds.
4. Write the solution set for the inequality.
STEP 3
Find the roots of the quadratic equation by factoring. We look for two numbers that multiply to and add to .
STEP 4
Set each factor equal to zero to find the roots.
STEP 5
Determine the intervals defined by the roots. The roots divide the number line into three intervals: , , and .
STEP 6
Test each interval to determine where the inequality holds. Choose a test point from each interval and substitute it into the inequality.
- For , choose :
- For , choose :
- For , choose :
STEP 7
Since the inequality holds in the interval , and the inequality is non-strict (), include the roots and in the solution set.
The solution set is:
The solution to the inequality is:
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