Learning Resources

Focus C: Solving Quadratic Inequalities

Method 1: Step 4

• You are exploring the effect multiplying (or dividing) by a negative number has on the property of inequalities. Notice what happens to the sign of the inequality when, for example, you multiply by -1. 
• Take the simple case of -x < 3. The solution set for this inequality would be all the numbers from -2 to infinity. Try some to verify. To solve the inequality for x, you would have to divide both sides by -1. If you then wrote x < -3, you would soon realize that the previous solution set no longer holds true. Substituting -2, for example, in for x creates a false statement. In order for the initial solution set to maintain its truth, you must change the sign of the inequality and write x > -3. All numbers from -2 to infinity will now satisfy this inequality. Try some to verify.