Algebra-2

To solve the equation 15 - 5|4x - 1| = -5, follow these steps:

Step 1: Isolate the Absolute Value

First, subtract 15 from both sides:

-5|4x - 1| = -5 - 15

-5|4x - 1| = -20

Next, divide both sides by -5:

|4x - 1| =

|4x - 1| = 4

 

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 = 4

 

2.Case 2:

4x - 1 = -4

 

Step 3: Solve Each Case

For Case 1:

4x - 1 = 4

Add 1 to both sides:

4x = 4 + 1

4x = 5

Now, divide by 4:

 

For Case 2:

4x - 1 = -4

Add 1 to both sides:

4x = -4 + 1

4x = -3

Now, divide by 4: