Which expression is equivalent to 4.8+2.2w – 1.4w+2.4
A.0.4(6+2w)
B.0.8(9+w)
C.1.6(3+2w)
D.3.6(2+w)
The Correct Answer and Explanation is:
To simplify the expression (4.8 + 2.2w – 1.4w + 2.4) and find its equivalent form, let’s go through each step carefully:
Step 1: Combine Like Terms
In the expression (4.8 + 2.2w – 1.4w + 2.4), there are two types of terms: those with the variable (w) and constant terms. We can simplify the expression by combining like terms.
- Combine terms with (w):
[
2.2w – 1.4w = 0.8w
] - Combine the constants:
[
4.8 + 2.4 = 7.2
]
So, the expression simplifies to:
[
7.2 + 0.8w
]
Step 2: Factor the Expression
To match the simplified expression with one of the answer choices, let’s factor out (0.8) from (7.2 + 0.8w):
[
7.2 + 0.8w = 0.8(9 + w)
]
Step 3: Check the Answer Choices
Looking at the answer choices:
- Option A: (0.4(6 + 2w))
- Option B: (0.8(9 + w))
- Option C: (1.6(3 + 2w))
- Option D: (3.6(2 + w))
The only option that matches our factored form (0.8(9 + w)) is Option B.
Final Answer:
The correct answer is B. (0.8(9 + w)).
Explanation:
The process of simplifying an algebraic expression involves combining like terms first, which reduces the number of terms in the expression. Here, the terms (2.2w) and (-1.4w) were combined to get (0.8w), while (4.8) and (2.4) were combined to yield (7.2). Factoring out the common term (0.8) from (7.2 + 0.8w) results in (0.8(9 + w)), which matches one of the answer choices. This method verifies that Option B is equivalent to the original expression and is therefore the correct answer.