Simplify 3 – (4x – 5) + 6. A) 12x + 21 B) 4x + 14 C) 4x + 4 D) -4x + 14
The Correct Answer and Explanation is:
To simplify the expression 3 – (4x – 5) + 6, let’s break it down step by step:
Step 1: Distribute the negative sign
In the expression 3 – (4x – 5) + 6, we have a negative sign outside the parentheses. To simplify, we distribute this negative sign to both terms inside the parentheses. 3−(4x−5)+6=3−4x+5+63 – (4x – 5) + 6 = 3 – 4x + 5 + 63−(4x−5)+6=3−4x+5+6
Notice that the negative sign in front of the parentheses changes the signs of both terms inside: -4x and +5.
Step 2: Combine like terms
Now we combine the constants (the numbers without variables) and the variable terms (those with x).
- Combine the constants:
3+5+6=143 + 5 + 6 = 143+5+6=14 - There is only one term with x, which is -4x. It stays the same.
Step 3: Write the simplified expression
Now that we’ve combined everything, we have the simplified expression: −4x+14-4x + 14−4x+14
Step 4: Conclusion
The simplified expression is -4x + 14, which corresponds to option D.
This simplification follows basic algebraic rules. The key step is recognizing the need to distribute the negative sign to the terms inside the parentheses, and then combining the like terms — constants and variables — to form the final simplified expression
