Question

How do you simplify $(2x + 8) + (3x + 7)$?

Answer 1

Hint: In this question, we need to simplify the given expression to obtain the solution. The given expression has two parts namely, terms with variables and constant terms. Firstly, we need to combine the like terms together. So combine the terms with the variable x in one parenthesis and the constant terms in another parenthesis. Then simplify the terms and obtain the solution.

Complete step by step answer:
Given the expression of the form $(2x + 8) + (3x + 7)$ …… (1)
We are asked to simplify the given expression and obtain the solution.
Note that the above expression has two parts which are terms with variable x and the constant terms.
In the given problem, the variable is x. We call it a variable because it can vary if we give different values to it. It will not remain the same. We can give a number of values to the variable x.
Whereas the constant terms will remain the same throughout the expression. That’s why constant terms are usually numbers.
In the equation (1), we note that $2x$ and $3x$ are variables with respect to x and 8, 7 are the constant terms.
Now consider $(2x + 8) + (3x + 7)$ .
Firstly, we make rearrangements in the above expression in such a way that combine the terms with variable x in one parenthesis and the remaining constant terms in the other parenthesis and simplify it.
Now combining terms with variables and constants, we get,
$ \Rightarrow (2x + 3x) + (8 + 7)$
Combining like terms $2x + 3x = 5x$
Combining like terms $8 + 7 = 15$
Hence we get,
$ \Rightarrow (5x) + (15)$
This can also be written without the parenthesis.
Thus, we have,
$ \Rightarrow 5x + 15$
Note that the number 5 is common throughout.
So factor out 5, we get,
$ \Rightarrow 5(x + 3)$
So the simplification of the given expression $(2x + 8) + (3x + 7)$ is equal to $5(x + 3)$.
$\therefore (2x + 8) + (3x + 7) = 5(x + 3)$.

Note: Students should not make any mistake in pairing the terms. They need to pair like terms together. They have to pair the terms in such a way that, terms with unknown variables as a one pair and terms with constant terms (numbers) as another pair. Each pair can be represented inside the parenthesis. Then they have to combine the like terms with the mathematical operation and simplify them. This method is easy and so avoid any mistakes in combining terms.