Which expression is equivalent to (5x + 3) + (4x + 7)?
The correct answer and explanation is:
✅ Correct Answer:
(5x + 3) + (4x + 7) = 9x + 10
✍️ Step-by-Step Explanation:
To simplify the expression (5x + 3) + (4x + 7), we are asked to combine like terms. Like terms are terms that have the same variable raised to the same power or constants (numbers without variables). Here’s how to approach it:
🔹 Step 1: Remove the parentheses
Since both sets of parentheses are preceded by a plus sign, you can simply drop the parentheses: (5x+3)+(4x+7)=5x+3+4x+7(5x + 3) + (4x + 7) = 5x + 3 + 4x + 7
🔹 Step 2: Group like terms
Now, group the terms with variables and constants: (5x+4x)+(3+7)(5x + 4x) + (3 + 7)
🔹 Step 3: Add the like terms
- Add the coefficients of xx:
5x+4x=9x5x + 4x = 9x - Add the constants:
3+7=103 + 7 = 10
🔹 Step 4: Write the simplified expression
9x+109x + 10
💡 Why This Matters:
This type of problem is an example of simplifying algebraic expressions, a core skill in algebra. It’s important in solving equations, understanding functions, and preparing for more complex math such as factoring, graphing, and calculus.
By simplifying expressions, you make them easier to work with and understand. This is a fundamental part of combining polynomials and helps develop your ability to think logically and mathematically.
📌 Summary:
The expression (5x+3)+(4x+7)(5x + 3) + (4x + 7)
is equivalent to 9x+10\boxed{9x + 10}