1 7 Solving AbsoluteValue Equations Warm Up Simplify

1 -7 Solving Absolute-Value Equations Warm Up Simplify. 1. x – 10 = 4 2. s + 5 = – 2 3. 32 = – 8 y 4. 5. – 14 = x – 5 6. 2 t + 5 = 45 Holt Mc. Dougal Algebra 1

1 -7 Solving Absolute-Value Equations Objectives Solve equations in one variable that contain ________-value expressions. Holt Mc. Dougal Algebra 1

1 -7 Solving Absolute-Value Equations Recall that the absolute-value of a number is that number’s distance from _______ on a number line. For example, |– 5| = 5 and |5| = 5. 5 units 6 5 4 3 2 1 0 1 2 3 4 5 6 For any _________ absolute value, there are exactly _____ numbers with that absolute value. For example, both 5 and – 5 have an absolute value of 5. 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 10 8 6 4 2 Holt Mc. Dougal Algebra 1 0 2 4 6 8 10 12

1 -7 Solving Absolute-Value Equations Additional Example 1 B: Solving Absolute-Value Equations Solve the equation. 3|x + 7| = 24 Holt Mc. Dougal Algebra 1

1 -7 Solving Absolute-Value Equations Check It Out! Example 1 a Solve the equation. |x| – 3 = 4 Holt Mc. Dougal Algebra 1

1 -7 Solving Absolute-Value Equations The table summarizes the steps for solving absolute-value equations. Solving an Absolute-Value Equation 1. 2. 3. 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 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 Holt Mc. Dougal Algebra 1

1 -7 Solving Absolute-Value Equations Check It Out! Example 3 Sydney Harbour Bridge is 134 meters tall. The height of the bridge can rise or fall by 180 millimeters because of changes in temperature. Write and solve an absolutevalue equation to find the minimum and maximum heights of the bridge. First convert millimeters to meters. 180 mm = 0. 180 m The height of the bridge can vary by 0. 18 m, so find two numbers that are 0. 18 units away from 134 on a number line. Holt Mc. Dougal Algebra 1

1 -7 Solving Absolute-Value Equations Check It Out! Example 3 Continued 133. 82 133. 88 Case 1 Holt Mc. Dougal Algebra 1 133. 94 134. 06 Case 2 134. 18