Question

How do you add the expression $\left( 2w-9 \right)+\left( 4w-5 \right)$ ?

Answer 1

Hint: Firstly, we need to add the same degree terms. Here, the same degree terms mean that these terms contain the same variable and same power to which it is raised to. These same degree terms have their numerical coefficients different. So, we Take out the variable common and add the numerical coefficient in the expression. Finally, evaluate and write them together.

Complete step by step solution:
The given expression is: $\left( 2w-9 \right)+\left( 4w-5 \right)$
Analyze the expression and determine the variable and their power.
First-term in the first expression that is $\left( 2w-9 \right)$ is $2w\;$ , which contains variable $w$ raised to the power one with the numerical coefficient $2$ . The second term is $-9$ which is a numerical coefficient with any variable with power zero.
First-term in the second expression that is $\left( 4w-5 \right)$ is $4w\;$ , which contains variable $w$ raised to the power one with the numerical coefficient $4$ . The second term is $-5$ which is a numerical coefficient with any variable with power zero.
Now rewrite the expression as below.
$\Rightarrow 2w-9+4w-5$
After grouping the same degree variables, we get,
$\Rightarrow 2w+4w-5-9$
As there are two terms with the same variable $w$ with the same degree which is one and with a different numerical coefficient that is $2$ and $4$ respectively, so we can take variable $w$ common and add their coefficients to add both the given expressions.
$\Rightarrow w\left( 2+4 \right)-5-9$
On further performing the addition operation, we get,
$\Rightarrow w\left( 6 \right)-5-9$
Which can be rewritten as,
$\Rightarrow 6w-5-9$
Since the rest of the terms other than $6w\;$ are numerical values, we can directly perform the given operations.
After evaluating we get,
$\Rightarrow 6w-14$
Hence the expression, $\left( 2w-9 \right)+\left( 4w-5 \right)$ on solving results to $6w-14$
Which on further taking out the common factor, $2$
We get, $2(3w-7)$

Note: The given expression is also known as a polynomial of degree one. Always the mathematical operations are to be done only on the same degree terms. The same degree terms have a different coefficient, so we take the variable common and then add the numerical coefficients in the usual way.