Which expression is equivalent to 9.8w + 6.4 + 6.7w -1.3?
Answer
A 21.6w
B 16.5w + 7.7
C 21.6
D 16.5w + 5.1
The correct answer and explanation is:
The correct answer is D: 16.5w + 5.1.
To solve this, combine like terms from the expression 9.8w+6.4+6.7w−1.39.8w + 6.4 + 6.7w – 1.3. First, identify the like terms:
- The terms with the variable ww are 9.8w9.8w and 6.7w6.7w.
- The constant terms are 6.46.4 and −1.3-1.3.
Step 1: Combine the terms with ww
Add 9.8w9.8w and 6.7w6.7w: 9.8w+6.7w=16.5w9.8w + 6.7w = 16.5w
Step 2: Combine the constant terms
Add 6.46.4 and −1.3-1.3: 6.4−1.3=5.16.4 – 1.3 = 5.1
Step 3: Write the simplified expression
Now that the like terms are combined, the simplified expression is: 16.5w+5.116.5w + 5.1
Thus, the correct answer is D: 16.5w + 5.1.
This process of combining like terms is essential in simplifying algebraic expressions. By grouping together terms with the same variable and constants separately, you make the expression easier to work with, whether you’re solving for the variable or just simplifying the equation.