Question

How do you simplify $2(v - 5) + 7v + 4$?

Answer 1

Hint: In this question, we need to simplify the given expression to obtain the solution. Here we need to combine the like terms together. Firstly, simplify the first term. Multiply the number 2 to $(v - 5)$ and simplify it. Then combine the terms with the variable $v$ in one parenthesis and the constant terms (numbers) in the other parenthesis. Then solve it to get the required solution.

Complete step by step solution:
Given an expression of the form,
$2(v - 5) + 7v + 4$ …… (1)
We are asked to simplify the above expression given in the equation (1).
We have to simplify in such a way that, first simplifying the first term and then simplifying the remaining terms. Then we combine the terms and simplify them together.
Now simplifying this expression by solving the expression in the first term.
Consider the first term given as, $2(v - 5)$.
Now multiplying the number 2, with each of the term in the parenthesis inside we get,
$ \Rightarrow 2(v - 5) = 2 \cdot v - 2 \cdot 5$
Simplifying this we get,
$ \Rightarrow 2(v - 5) = 2v - 10$
Now adding the first term with the remaining terms.
Hence the equation (1) becomes,
$ \Rightarrow 2v - 10 + 7v + 4$
Rearranging the above expression in such a way that the terms with the variable $v$ in one parenthesis and the constant terms in the other parenthesis.
Hence we get,
$ \Rightarrow (2v + 7v) + (- 10 + 4)$
Combining the like terms $2v + 7v = 9v$
Combining the like terms $ - 10 + 4 = - 6$
Hence we have,
$ \Rightarrow 9v + (- 6)$
This can be written as,
$ \Rightarrow 9v - 6$
Note that the number 3 is a multiple of both the numbers 9 and 6.
Therefore, factor out 3 we get,
$ \Rightarrow 3(3v - 2)$

Hence the simplified form of the expression $2(v - 5) + 7v + 4$ is given by $3(3v - 2)$.

Note: Students may go wrong in combining the terms. They must be careful while simplifying the given expression. Remember to combine the like terms together.
Combine the terms containing the unknown variable in one parenthesis and then combine the constant terms in the other parenthesis. Then simplify the expression inside the parenthesis carefully and solve to obtain the desired result.
We must know the distributive property to solve such problems.
The distributive property for addition and subtraction is given below.
(1) $x \cdot (y + z) = x \cdot y + x \cdot z$
(2) $x \cdot (y - z) = x \cdot y - x \cdot z$