Algebra-2

To solve the equation |4x + 1| + 8 = 18, we first isolate the absolute value expression.

Step 1: Isolate the Absolute Value

Subtract 8 from both sides:

|4x + 1| = 18 - 8

|4x + 1| = 10

 

Step 2: Set Up Cases for Absolute Value

Now, we can set up two cases based on the definition of absolute value:

1.Case 1:

4x + 1 = 10

 

2.Case 2:

4x + 1 = -10

 

Step 3: Solve Each Case

For Case 1:

4x + 1 = 10

Subtract 1 from both sides:

4x = 10 - 1

4x = 9

Now, divide by 4:

 

For Case 2:

4x + 1 = -10

Subtract 1 from both sides:

4x = -10 - 1

4x = -11

Now, divide by 4: