Question

How do you subtract, $\left( 4x-6 \right)$ from $\left( 2x+8 \right)$ ?

Answer 1

Hint: We have been asked to perform one of the four fundamental mathematical operations, that is, subtraction. Subtraction is basically an operation where the value of one entity is deducted from the value of another entity. Here, we have the two entities as variables and not certain numbers that have constant values, but still the basis of subtraction remains the same.

Complete step-by-step solution:
Let us first assign some terms that we are going to use in our solution. Let us denote the two terms involved in subtraction be ‘a’ and ‘b’, such that we have:
$\Rightarrow a=4x-6$
$\Rightarrow b=2x+8$
Then, we need to find the value of the expression: $\left( b-a \right)$
Now, according to the problem, we have to subtract ‘a’ from ‘b’. So, the term ‘b’ will be written first, that is, ‘b’ is the term from which something is to be deducted. Therefore, it makes ‘a’ the second term in our operation, that is, the term that has to be deducted from ‘b’. This statement can be mathematically written as:
$\Rightarrow b-a=\left( 2x+8 \right)-\left( 4x-6 \right)$
Here, the operation will be carried out between like terms only, that is, constant with constant and variable with variable. Thus, our equation can be simplified into:
$\begin{align}
  & \Rightarrow b-a=2x+8-4x+6 \\
 & \therefore b-a=14-2x \\
\end{align}$
Hence, $\left( 4x-6 \right)$ when subtracted from $\left( 2x+8 \right)$ comes out to be $\left( 14-2x \right)$.

Note: While performing subtraction of two constants or two variables or even one constant and one variable, we should always check the sign of all the individual terms at each step of the process. This is one of the best ways to verify our solution. Also, one should be very careful while performing these rather “easy” calculations and not concur any error just to be quick.