Question

How do you simplify $\left( 6x+14 \right)-\left( 9x+5 \right)$?

Answer 1

Hint: We first try to remove the brackets. Then we separate the variables and the constants of the equation $\left( 6x+14 \right)-\left( 9x+5 \right)$. We apply the binary operation of addition for both variables and constants. The solutions of the variables and the constants will be added at the end to get the final answer.

Complete step by step answer:
The given equation $\left( 6x+14 \right)-\left( 9x+5 \right)$ is a linear equation of x. we need to simplify the equation by solving the variables and the constants separately.
We first try to remove the brackets. As the sign before the one of the brackets is negative that’s why the sign of the terms change.
$\left( 6x+14 \right)-\left( 9x+5 \right)=6x+14-9x-5$
All the terms in the equation of $6x+14-9x-5$ are either variable of x or a constant. We first separate the variables.
There are two such variables which are $6x$ and $-9x$. The signs of the variables are positive and negative respectively with coefficients being 6 and $-9$ respectively.
The binary operation between them is addition which gives us $6x-9x=-3x$.
Now we take the constants.
There are two such constants which are 14 and $-5$. The signs of the variables are positive and negative respectively.
The binary operation between them is addition which gives us $14+\left( -5 \right)=14-5=9$.

The final solution becomes $6x+14-9x-5=-3x+9$

Note: We can verify the result of the equation $\left( 6x+14 \right)-\left( 9x+5 \right)=-3x+9$ by taking an arbitrary value of x as $x=2$.
Therefore, the left-hand side of the equation becomes
$\left( 6x+14 \right)-\left( 9x+5 \right)=\left( 6\times 2+14 \right)-\left( 9\times 2+5 \right)=26-23=3$
The right-hand side of the equation is $-3x+9=\left( -3 \right)\times 2+9=3$.
Thus, verified the equation $\left( 6x+14 \right)-\left( 9x+5 \right)=-3x+9$.