Question

By how much is $2x-3y+4z$ greater than $2x+5y-6z+2$?

Answer 1

Hint: We first evaluate the greater and lesser term. Then we find the increment by subtracting the lesser term from the other. The solution of the subtraction gives us the final solution.

Complete step by step solution:
It has been given that the value of $2x-3y+4z$ greater than $2x+5y-6z+2$.
We have to find the value of the increment form $2x+5y-6z+2$ to $2x-3y+4z$.
The increment can be found from the difference of the numbers $2x-3y+4z$ and $2x+5y-6z+2$.
Therefore, we have to subtract $2x+5y-6z+2$ from $2x-3y+4z$.
The mathematical form will be $\left( 2x-3y+4z \right)-\left( 2x+5y-6z+2 \right)$.
We have to calculate the coefficients of the same variable.
Simplifying we get $\left( 2x-3y+4z \right)-\left( 2x+5y-6z+2 \right)=2x-3y+4z-2x-5y+6z-2$.
We take the coefficients of variable x and get $2x-2x=0$.
We take the coefficients of variable y and get $-3y-5y=-8y$.
We take the coefficients of variable x and get $4z+6z=10z$.
There remains only one constant which is $-2$.
The simplified form of the subtraction is $-8y+10z-2$.
Therefore. $2x-3y+4z$ is greater than $2x+5y-6z+2$ by $-8y+10z-2$.

Note: We need to be careful about which we have to subtract from whom. The question was about the value by which $2x-3y+4z$ is greater than $2x+5y-6z+2$. It was an obvious choice that we need to subtract $2x+5y-6z+2$ from $2x-3y+4z$.