Algebra-2

To solve the equation |4x + 1| = 9, we will break it down into two cases based on the definition of absolute value.

Step 1: Set Up Cases for Absolute Value

The equation |4x + 1| = 9 leads us to two cases:

1.Case 1:

4x + 1 = 9

 

2.Case 2:

4x + 1 = -9

 

Step 2: Solve Each Case

For Case 1:

4x + 1 = 9

Subtract 1 from both sides:

4x = 9 - 1

4x = 8

Now, divide by 4:

x = 2

 

For Case 2:

4x + 1 = -9

Subtract 1 from both sides:

4x = -9 - 1

4x = -10

Now, divide by 4:

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