Solving absolute value equation

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SUMMARY

The absolute value equation ##\left | r-5 \right | = \left | r+2 \right |## can be solved analytically by considering two cases: when both expressions are of the same sign (either both positive or both negative) and when they are of opposite signs. The final solution is the union of the solution sets derived from these two cases. This method provides a systematic approach to solving similar absolute value equations.

PREREQUISITES
  • Understanding of absolute value functions
  • Familiarity with algebraic equations
  • Knowledge of solving linear equations
  • Ability to analyze cases in mathematical problems
NEXT STEPS
  • Study the properties of absolute value functions
  • Learn techniques for solving linear equations
  • Explore case analysis in algebra
  • Practice solving various absolute value equations
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Students, educators, and anyone looking to enhance their skills in solving absolute value equations and algebraic expressions.

Mr Davis 97
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I have the following equation: ##\left | r-5 \right | = \left | r+2 \right |##.

What is a general, analytical way that I can solve equations like these? I always get stumped when trying to solve them...
 
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Mr Davis 97 said:
I have the following equation: ##\left | r-5 \right | = \left | r+2 \right |##.

What is a general, analytical way that I can solve equations like these? I always get stumped when trying to solve them...
Look at two cases:
1. Both expressions are the same sign; i.e., both are positive or both are negative.
2. The two expressions are opposite in sign.

The solution to the original equation is the union of the solution sets for the two cases.
 
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