171 1.7 Inequalities 5 0 7 3 – Figure 11 EXAMPLE 4 Solving a Three-Part Inequality Solve -2 65 + 3x 620. Give the solution set in interval notation. SOLUTION -2 6 5 + 3x 620 -2 - 5 65 + 3x - 5 620 - 5 Subtract 5 from each part. -7 6 3x 615 Combine like terms in each part. -7 3 6 3x 3 6 15 3 Divide each part by 3. - 7 3 6 x 65 The solution set, graphed in Figure 11, is the interval A - 7 3 , 5B. S Now Try Exercise 29. Quadratic Inequalities We can distinguish a quadratic inequality from a linear inequality by noticing that it is of degree 2. Quadratic Inequality A quadratic inequality is an inequality that can be written in the form ax2 +bx +c *0,* where a, b, and c are real numbers and a≠0. *The symbol 6 can be replaced with 7, …, or Ú. One method of solving a quadratic inequality involves finding the solutions of the corresponding quadratic equation and then testing values in the intervals on a number line determined by those solutions. Solving a Quadratic Inequality Step 1 Solve the corresponding quadratic equation. Step 2 Identify the intervals determined by the solutions of the equation. Step 3 Use a test value from each interval to determine which intervals form the solution set. EXAMPLE 5 Solving a Quadratic Inequality Solve x2 - x - 12 60. SOLUTION Step 1 Find the values of x that satisfy x2 - x - 12 = 0. x2 - x - 12 = 0 Corresponding quadratic equation 1x + 321x - 42 = 0 Factor. x + 3 = 0 or x - 4 = 0 Zero-factor property x = -3 or x = 4 Solve each equation.
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