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By Mary Jane Sterling

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Example text

For example, when x = 5, you get 25 – 5 = 20. That’s certainly bigger than 12, so the number 5 works; x = 5 is a solution. How about the number 2? When x = 2, you get 4 – 2 = 2, which isn’t bigger than 12. You can’t use x = 2 in the solution. Do you then conclude that smaller numbers don’t work? Not so. When you try x = –10, you get 100 + 10 = 110, which is most definitely bigger than 12. You can actually find infinitely many numbers that make this inequality a true statement. Chapter 3: Making Quick Work of Quadratic Equations 31 Therefore, you need to solve the inequality by using the steps I outline in the introduction to this section: 1.

I’ll show you the step-by-step process with this example: Solve for x in . 1. Find a common denominator. The LCD is a multiple of each of the original denominators. To solve this equation, use 4(2x – 3) as the LCD. All three denominators divide this product evenly. Chapter 4: Rolling Along with Rational and Radical Equations 37 2. Write each fraction with the common denominator. Multiply each fraction by the equivalent of 1. The numerator and denominator are the same, and the denominator is what is needed to change the original denominator into the LCD: Completing the multiplication: 3.

4. You can see the two numbers on a number line in the following illustration. −6 2 Chapter 3: Making Quick Work of Quadratic Equations 33 5. Create a sign line for the two zeroes. You can see in the following figure that the numerator is positive when x is greater than 2, and the denominator is positive when x is greater than –6. (−) (−) (−) (+) (+) (+) 2 −6 6. When determining the solution, keep in mind that the inequality calls for something less than or equal to zero. The fraction is a negative number when you choose an x between –6 and 2.

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