2-5 Study Guide and Intervention Solving Equations Involving Absolute Value Absolute Value Equations When solving equations that involve absolute value, there are two cases to consider. Case 1: The inside the absolute value symbols is positive. Case 2: The value inside the absolute value symbols is negative. Example 1: Solve + = 1. Then graph the solution set. Example 2: Write an equation involving absolute value for the graph. Write + = 1 as + 4 = 1 or + 4 = x x –1. + 4 = 1 or + 4 = x x –1 Find the point that is the same distance from as it is –2 + 4 4 = 1 4 + 4 4 = 4 x x – – – –1 – from 4. = = x x –3 –5 The solution set is {–5, –3}. The distance from 1 to is 3 units. The distance from –2 The is shown below. 1 to 4 is 3 units. So, = 3. – Exercises Solve each equation. Then graph the solution set. = 3 1. 2. = 4 – 3. + = 2 4. + 2 = 3 2 = 5 5. – 6. + 2 = 4 7. = 8 8. = 7 – 9. = 0.5 – 10. = 50 – 11. = 11 – 12. + = 6 Write an equation involving absolute value for each graph. 13. 15. 14.
2-5 Study Guide and Intervention Solving Equations Involving Absolute Value Absolute Value Equations When solving equations that involve absolute value, there are two cases to consider. Case 1: The inside the absolute value symbols is positive. Case 2: The value inside the absolute value symbols is negative. Example 1: Solve + = 1. Then graph the solution set. Write + = 1 as x + 4 = 1 or x + 4 = –1. x + 4 = 1 or x + 4 = –1 x + 4 – 4 = 1 – 4 x + 4 – 4 = –1 – 4 x = –3 x = –5 The solution set is {–5, –3}. The is shown below. Example 2: Write an equation involving absolute value for the graph. Find the point that is the same distance from –2 as it is from 4. The distance from 1 to –2 is 3 units. The distance from 1 to 4 is 3 units. So, – = 3. Exercises Solve each equation. Then graph the solution set. 1. = 3 4. + 2 = 3 7. = 8 10. – = 50 2. – = 4 5. – 2 = 5 8. – = 7 11. – = 11 3. + = 2 6. + 2 = 4 9. – = 0.5 12. + = 6 Write an equation involving absolute value for each graph. 13. 14. 15.
day_12-_sgi_equations_with_absolute_value.docx