Question

What is the factorisation of $7x-42$?

Answer 1

Hint: We first explain the process of factorisation which is available for $7x-42$. We find the GCD of 7 and 42 to take it as common from the constants. We form the equation $7x-42$ as the multiplication of a constant and linear equation.

Complete step-by-step solution:
The given equation $7x-42$ is a linear equation of $x$.
We need to factorise the equation.
The only process that is available for this equation to factorise is to take a common constant out of the terms 42 and $7x$.
Now we are actually taking the constant from 7 and 42. We are finding the maximum possible constant to take out. It will be the greatest common divisor of the numbers 7 and 42.
Now, we need to find the GCD of 7 and 42.
$\begin{align}
  & 7\left| \!{\underline {\,
  7,42 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,6 \,}} \right. \\
\end{align}$
Therefore, the GCD will be 7.
We are taking 7 as common from the numbers 42 and $7x$.
If we take 7 from 42, the remaining number will be $\dfrac{42}{7}=6$.
If we take 7 from $7x$, the remaining number will be $\dfrac{7x}{7}=x$.
Now the common term 7 will form the multiplication of two terms. One being 7 and the other being the addition of 6 with $x$. Therefore, the factorisation is $7x-42=7\left( x-6 \right)$.

Note: We can verify the result of the factorisation by taking an arbitrary value of x where $x=2$.
We put $x=2$ on the left-hand side of the equation $7x-42$ and get
$7x-42=7\times 2-42=14-42=-28$
Now we put $x=2$ on the right-hand side of the equation $7\left( x-6 \right)$ and get
$7\left( x-6 \right)=7\left( 2-6 \right)=7\times \left( -4 \right)=-28$. Thus, verified the factorisation $7x-42=7\left( x-6 \right)$.