Question

Add the following expressions: 5x, 7x, -6x

Answer 1

Hint: Here, we need to add the three terms 5x, 7x and -6x. Here, the variables of all the three terms are the same so we can add the terms by adding the coefficients of the variables. Here, first we will take out x as common and then add the coefficients of the terms. Hence, we will get the addition of all three terms.

Complete step-by-step solution:
In this question, we are given three terms 5x, 7x and -6x and we have to add these terms.
Now, here the variable is the same for all the terms that is x. So we can add these terms by adding the coefficients of these variables.
So, the addition of 5x, 7x and -6x will be
$ \Rightarrow $Addition of 5x, 7x and -6x$ = 5x + 7x - 6x$- - - - - - - - - - - (1)
Now, we can take x as common. So, taking x as common, equation (1) will become
$ \Rightarrow $Addition of 5x, 7x and -6x$ = \left( {5 + 7 - 6} \right)x$ - - - - - - - - - - - - - (2)
Now, simply add all the three terms. So, equation (2) will become
$ \Rightarrow $Addition of 5x, 7x and -6x$ = \left( 6 \right)x = 6x$
Hence, the addition of the terms 5x, 7x and -6x will be equal to 6x.

Note: The terms having the same variables are called like terms and the terms having different variables are called unlike terms. Note that you can only add or subtract terms if they are like and you cannot add or subtract them if they are unlike.