How do you answer this problem: 4.2v – 5 – 6.5v

How do you answer this problem: 4.2v – 5 – 6.5v?

The Correct Answer and Explanation is:

To solve the algebraic expression:

4.2v – 5 – 6.5v

Step-by-step solution:

1. Group like terms:
   Like terms are terms that have the same variable part. Here, 4.2v and -6.5v are like terms because they both contain the variable v. The constant -5 stands alone.
2. Combine the variable terms: 4.2v−6.5v=−2.3v4.2v – 6.5v = -2.3v4.2v−6.5v=−2.3v
3. Now rewrite the expression with the simplified variable term: −2.3v−5-2.3v – 5−2.3v−5

This is the simplified form of the expression:
Answer: −2.3v−5-2.3v – 5−2.3v−5

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Explanation:

In algebra, simplifying expressions is a fundamental skill. The expression provided, 4.2v – 5 – 6.5v, includes two types of terms: variable terms (4.2v and -6.5v) and a constant term (-5). The goal is to simplify the expression by combining like terms.

Like terms are terms that have the same variable raised to the same power. Here, both 4.2v and -6.5v are like terms because they involve the same variable v. We can add or subtract like terms by combining their coefficients (the numbers in front of the variables).

To combine 4.2v and -6.5v, subtract the coefficients:4.2−6.5=−2.34.2 – 6.5 = -2.34.2−6.5=−2.3

So, 4.2v - 6.5v becomes -2.3v.

The constant term -5 is not a like term with v terms, so it cannot be combined with them. It remains separate in the simplified expression.

Thus, the simplified expression is:−2.3v−5-2.3v – 5−2.3v−5

This expression means that the variable part is reduced to negative 2.3 times v, and 5 is subtracted afterward. This simplified form is easier to work with and is crucial in solving equations, graphing lines, or performing further algebraic operations. Mastering this process helps develop strong problem-solving skills and prepares students for more complex math in the future.