Simplify (3x – 4)-(5x -3).
-2r
-2x -1
2x -1
2x-7
The Correct Answer and Explanation is:
Simplified Answer:
To simplify the expression:
(3x – 4) – (5x – 3)
Step 1: Distribute the minus sign to the second set of parentheses:
= 3x – 4 – 5x + 3
Step 2: Combine like terms:
- Combine the x terms: 3x – 5x = -2x
- Combine the constants: -4 + 3 = -1
Final answer: -2x – 1
✅ Correct option: -2x – 1
Explanation:
To simplify an algebraic expression like (3x – 4) – (5x – 3), we follow basic algebra rules for combining like terms and handling parentheses.
Step 1: Understanding the structure
The expression is composed of two binomials: (3x – 4) and (5x – 3). The minus sign in between them means we are subtracting the entire second binomial from the first. This is crucial — we must subtract both terms in the second group.
Step 2: Remove the parentheses
Since we are subtracting the second group, we must distribute the minus sign (which is equivalent to multiplying by -1). This changes the sign of every term inside the second parentheses:
- From (5x – 3), we get -5x + 3
Now rewrite the expression:
3x – 4 – 5x + 3
Step 3: Combine like terms
Group terms with the same variable or type:
- Variables: 3x – 5x = -2x
- Constants: -4 + 3 = -1
Putting them together, we get the simplified expression:
-2x – 1
This is the cleanest, most simplified form — no parentheses, no further combining possible.
Common Mistakes to Avoid:
- Forgetting to distribute the minus sign to both terms in the second group.
- Combining unlike terms (e.g., constants and variables).
- Reversing signs incorrectly during distribution.
Understanding these steps ensures clarity when simplifying expressions and builds a strong foundation for solving more complex algebraic problems.
