Question

How do you combine like terms in $8x-2-5x+7$?

Answer 1

Hint: First we will assume the given expression as E. Now, we will group the terms containing the variable x together. Similarly we will group the constant terms together. In the next step we will simplify the expression using simple addition or subtraction, whichever required, to get the answer.

Complete step by step solution:
Here, we have been provided with the expression: $8x-2-5x+7$ and we are asked to combine the like terms. That means we need to combine the terms containing the variable separately and the constant terms separately.
First let us assume the given expression as E, so we have,
$\Rightarrow E=8x-2-5x+7$
In the above expression we can see that there are four terms in which two of them contain the variable x and two are constants, so we have to group the terms containing the variable x together and simplify them and similarly group the constant terms together and simplify them separately. So, we have on grouping,
$\Rightarrow E=\left( 8x-5x \right)+\left( -2+7 \right)$
On performing simple subtraction we get,
$\begin{align}
  & \Rightarrow E=\left( 3x \right)+\left( 5 \right) \\
 & \Rightarrow E=3x+5 \\
\end{align}$

Hence, the simplified value of the given expression is $3x+5$.

Note: Note that we cannot simplify the expression further because we cannot form a particular number with the terms of the expression $3x+5$. To get a particular number we need to assign a fixed real number to the variable x. One thing to notice is that actually there are not four terms but only two terms in the expression. We cannot judge the number of terms before simplifying the expression.