1 7 AbsoluteValue Equations Solving AbsoluteValue Equations 1
1 -7 Absolute-Value Equations Solving Absolute-Value Equations 1 -7 Solving Warm Up Lesson Presentation Lesson Quiz Holt Mc. Dougal Holt. Algebra Mc. Dougal Algebra 11 Holt 1 Algebra
1 -7 Solving Absolute-Value Equations Objectives Solve equations in one variable that contain absolute-value expressions. Holt Mc. Dougal Algebra 1
1 -7 Solving Absolute-Value Equations Holt Mc. Dougal Algebra 1
1 -7 Solving Absolute-Value Equations Additional Example 1 A: Solving Absolute-Value Equations Solve the equation. |x| = 12 Think: What numbers are 12 units from 0? • 12 units 12 10 8 6 4 2 Case 1 x = 12 Case 2 x = – 12 • 0 12 units 2 6 • 8 10 12 Rewrite the equation as two cases. The solutions are {12, – 12}. Holt Mc. Dougal Algebra 1 4
1 -7 Solving Absolute-Value Equations Check It Out! Example 1 a Solve the equation. |x| – 3 +3 |x| Case 1 x=7 =4 =4 +3 =7 Since 3 is subtracted from |x|, add 3 to both sides. Think: What numbers are 7 units from 0? Case 2 Rewrite the equation as two x = – 7 cases. The solutions are {7, – 7}. Holt Mc. Dougal Algebra 1
1 -7 Solving Absolute-Value Equations Check It Out! Example 1 b Solve the equation. 8 =|x 2. 5| Case 1 8 = x 2. 5 +2. 5 10. 5 = x Think: What numbers are 8 units from 0? Rewrite the equations as two cases. Case 2 8 = x 2. 5 +2. 5 Since 2. 5 is subtracted from x add 2. 5 to both 5. 5 = x sides of each equation. The solutions are {10. 5, – 5. 5}. Holt Mc. Dougal Algebra 1
1 -7 Solving Absolute-Value Equations Additional Example 1 B: Solving Absolute-Value Equations Solve the equation. 3|x + 7| = 24 |x + 7| = 8 Since |x + 7| is multiplied by 3, divide both sides by 3 to undo the multiplication. Think: What numbers are 8 units from 0? Case 2 Case 1 Rewrite the equations as two x + 7 = 8 x + 7 = – 8 cases. Since 7 is added to x – 7 – 7 subtract 7 from both sides of x =1 x = – 15 each equation. The solutions are {1, – 15}. Holt Mc. Dougal Algebra 1
1 -7 Solving Absolute-Value Equations Additional Example 2 A: Special Cases of Absolute. Value Equations Solve the equation. 8 = |x + 2| 8 +8 +8 0 = |x + 2| Since 8 is subtracted from |x + 2|, add 8 to both sides to undo the subtraction. 0= x+2 2 = x There is only one case. Since 2 is added to x, subtract 2 from both sides to undo the addition. The solution is { 2}. Holt Mc. Dougal Algebra 1
1 -7 Solving Absolute-Value Equations Additional Example 2 B: Special Cases of Absolute. Value Equations Solve the equation. 3 + |x + 4| = 0 3 3 |x + 4| = 3 Since 3 is added to |x + 4|, subtract 3 from both sides to undo the addition. Absolute value cannot be negative. This equation has no solution. Holt Mc. Dougal Algebra 1
1 -7 Solving Absolute-Value Equations Remember! Absolute value must be nonnegative because it represents a distance. Holt Mc. Dougal Algebra 1
1 -7 Solving Absolute-Value Equations Check It Out! Example 2 a Solve the equation. 2 |2 x 5| = 7 2 2 |2 x 5| = 5 Since 2 is added to –|2 x – 5|, subtract 2 from both sides to undo the addition. Since |2 x – 5| is multiplied by negative 1, divide both sides by negative 1. Absolute value cannot be negative. This equation has no solution. Holt Mc. Dougal Algebra 1
1 -7 Solving Absolute-Value Equations Check It Out! Example 2 b Solve the equation. 6 + |x 4| = 6 +6 +6 |x 4| = 0 x 4 = 0 + 4 +4 x Holt Mc. Dougal Algebra 1 = 4 Since – 6 is added to |x 4|, add 6 to both sides. There is only one case. Since 4 is subtracted from x, add 4 to both sides to undo the addition.
1 -7 Solving Absolute-Value Equations Lesson Quiz Solve each equation. 1. 15 = |x| – 15, 15 2. 2|x – 7| = 14 0, 14 3. |x + 1|– 9 = – 9 – 1 4. |5 + x| – 3 = – 2 – 6, – 4 5. 7 + |x – 8| = 6 no solution 6. Inline skates typically have wheels with a diameter of 74 mm. The wheels are manufactured so that the diameters vary from this value by at most 0. 1 mm. Write and solve an absolute-value equation to find the minimum and maximum diameters of the wheels. |x – 74| = 0. 1; 73. 9 mm; 74. 1 mm Holt Mc. Dougal Algebra 1
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