Algebra-2

To solve the equation |4 - 3x| = 5, we can break it down into two cases based on the definition of absolute value.

Step 1: Set Up Cases for Absolute Value

The equation |4 - 3x| = 5 gives us two cases:

1.Case 1:

4 - 3x = 5

 

2.Case 2:

4 - 3x = -5

 

Step 2: Solve Each Case

For Case 1:

4 - 3x = 5

Subtract 4 from both sides:

-3x = 5 - 4

-3x = 1

Now, divide by -3:

 

For Case 2:

4 - 3x = -5

Subtract 4 from both sides:

-3x = -5 - 4

-3x = -9

Now, divide by -3:

x = 3

 

Step 3: Write the Solutions

The solutions to the equation |4 - 3x| = 5 are:

Click "Show Answer" to reveal the answer and analysis