Question

How do you factor $-3x-4x$?

Answer 1

Hint: We first explain the process of factorisation which is available for $-3x-4x$. We find the GCD of 3 and 4 to take it as common from the constants. We can also take the variable $x$ as common. We form the equation $-3x-4x$ as the multiplication of constants and variables.

Complete step by step answer:
The given equation $-3x-4x$ 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 and a variable.
Now we take the constant from 3 and 4. We are finding the maximum possible constant to take out.
Now, we need to find the GCD of 3 and 4. These are co-primes. So, the GCD is 1.
We can take the negative sign as common.
The sign taking common can be termed as taking the common constant term of $-1$.
Now we can see we can take the variable a common. Both have $x$ as common.
So, $-3x-4x=-x\left( 3+4 \right)$.
The simplified form is $-3x-4x=-x\left( 3+4 \right)=-7x$
Therefore, the factorisation of $-3x-4x$ is $-x\left( 3+4 \right)$.

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 $-3x-4x$ and get
$-3x-4x=-3\times 2-4\times 2=-6-8=-14$
Now we put $x=2$ on the right-hand side of the equation $-x\left( 3+4 \right)$ and get
$-x\left( 3+4 \right)=\left( -2 \right)\times 7=-14$.
Thus, verified the factorisation $-3x-4x=-x\left( 3+4 \right)$.