# How do you solve #abs(2x+1)=5#?

See a solution process below:

Since the absolute value function takes any term and converts it to a non-negative form, we have to solve the term for both its positive and negative equivalent within the absolute value function.

First Solution:

Option 2:

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So hence;

Thus, after resolving the two linear equations, we obtain;

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To solve the equation (|2x+1|=5), you'll need to consider two cases:

- (2x+1) is positive and equal to 5.
- (2x+1) is negative and equal to -5.

Solve each case separately for (x).

Case 1: [2x+1=5] [2x=5-1] [2x=4] [x=\frac{4}{2}] [x=2]

Case 2: [2x+1=-5] [2x=-5-1] [2x=-6] [x=\frac{-6}{2}] [x=-3]

So, the solutions to the equation are (x=2) and (x=-3).

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