Solving Absolute Value Equations – Two Solutions!

 



Absolute value equations require considering multiple cases. Here's a quick guide to solving them.

Problem:
Solve the absolute value equation ∣2x+1∣=7|2x + 1| = 7.

Solution:

  1. For 2x+1=72x + 1 = 7:
    2x=6⇒x=32x = 6 \Rightarrow x = 3
  2. For 2x+1=−72x + 1 = -7:
    2x=−8⇒x=−42x = -8 \Rightarrow x = -4

Thus, the solutions are x=3x = 3 and x=−4x = -4.

Conclusion:
Remember, absolute value equations always produce two possible solutions. Set up each case and solve accordingly.

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