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 $|2x + 1| = 7$.

Solution:

1. For $2x + 1 = 7$:
   $2x = 6 \Rightarrow x = 3$
2. For $2x + 1 = -7$:
   $2x = -8 \Rightarrow x = -4$

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

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