What happens to the equation 4x - x + 6 + 8 without like terms?

• A. It remains unchanged
• B. It becomes 4x + 14
• C. It becomes 3x + 14
• D. It becomes 5x + 14

Answer: (C)

To understand why the equation 4x - x + 6 + 8 simplifies to 3x + 14, let’s look at the process of combining like terms in this expression.

First, identify the like terms in the equation. The terms containing the variable (x) are 4x and -x, while the constant terms are 6 and 8.

When you combine the like terms for the variable (x):

• Start with 4x.

• Subtract x, which is equivalent to -1x.

This calculation leads to:

4x - x = 4x - 1x = 3x.

Next, combine the constant terms:

• The constants are 6 and 8.

• Adding these gives: 6 + 8 = 14.

Putting these together, the expression simplifies to:

3x + 14.

This is why the result of simplifying the equation is 3x + 14, demonstrating the fundamental principle of combining like terms in algebraic expressions.