5.3 solving abs value equations
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Absolute value equations can have two solutions, as they are equivalent to two separate equations where the absolute value is equal to the number or its negative. To solve absolute value equations, they are rewritten as two separate equations and then solved, with the answer written with both possible solutions separated by "or". More complex absolute value equations may require isolating the term inside the absolute value before splitting into two equations.
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5.3 solving abs value equations
- 2. Absolute value equations can have two solutions. For example: |x| = 5 has solutions x = 5 or x = -5
- 3. 1. Rewrite as two equations |x| = c or |x| = -c 2. Solve both equations 3. Write answer: x = __ or x = __ Example: |-2x| = 6
- 4. Solve |2x – 5| = 9
- 5. Solve |x – 3| = -4
- 6. Solve |6x – 3| = 15
- 7. Sometimes, before writing 2 equations, we must isolate the “absolute value part” of the equation. Example: -3|x + 1| = -9
- 8. Solve |2x – 6| + 7 = 13
- 9. Solve 4|2 – x| = 12
- 10. Solve 2 – 5|5x – 5| = -73
- 11. Solve 3|3 – 5x| - 3 = 18