Solve the equation .
Solve the inequality by following steps:
step0: Solve the inequality by testing the values in the interval:
step1: Rewrite the expression:
step2: Move the constant to the right side:
step3: Remove 0:
step4: Simplify the expression:
step5: Simplify:
step6: Separate into possible cases:
step7: Determine the test intervals:
step8: Choose a value:
step9: Test the chosen value:
step10: Include the critical value:
step11: The final solution is
The solution to the inequality is .
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The Deep Dive
To solve the inequality , we can factor it as . This means we need to find the values of where the product of these two factors is non-negative. The critical points are and , which divides the number line into three intervals: , , and . Testing values from each interval shows that the solution set is or .
To visualize this, think of a number line and the two points where the expression equals zero. The inequality is satisfied to the left of -2 and to the right of 2, like two happy zones on the number line! Just remember, the points where the expression equals zero are part of the solution, like plus signs on either end!