Algebra-2

To solve the equation |3x + 1| = 4 - x, we will consider two cases based on the definition of absolute value.

Case 1: 3x + 1 = 4 - x

Solve for x:

3x + 1 = 4 - x

Add x to both sides:

3x + x + 1 = 4

Combine like terms:

4x + 1 = 4

Subtract 1 from both sides:

4x = 3

Divide by 4:

 

Case 2: 3x + 1 = -(4 - x)

Solve for x:

3x + 1 = -4 + x

Subtract (x) from both sides:

3x - x + 1 = -4

Combine like terms:

2x + 1 = -4

Subtract 1 from both sides:

2x = -5

Divide by 2:

 

Solutions Found

The potential solutions are:

 

Step 3: Check for Extraneous Solutions

Check

Substituting into the original equation:

Left side:

 

Right side:

Since both sides are equal,

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