Question

Simplify each expression

$3x+4y-5x$

Short answer

$3x+4y-5x$ is simplified to$-2\left(x-2y\right)$

Step-by-step solution

- Write properties of real numbers 

Properties of real numbers are written in following table:

For any real numbers a, b, and c:
Property	Addition	Multiplication
Commutative	$a+b=b+a$	$a·b=b·a$
Associative	$\left(a+b\right)+c=a+\left(b+c\right)$	$\left(a·b\right)·c=a·\left(b·c\right)$
Identity	$a+0=a=0+a$	$a·1=a=1·a$
Inverse	$a+\left(-a\right)=0=\left(-a\right)+a$	If $a\ne 0$, then $a·\frac{1}{a}=1=\frac{1}{a}·a$
Distributive	$a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$

- Simplify by grouping same variables

To simplify given equation, first use commutative property of addition then distributive property to group coefficients of same variable as shown below

$\begin{array}{c}3x+4y-5x=3x-5x+4y\\ =\left(3-5\right)x+4y\end{array}$

- Use distributive property 

Firstly simplify parentheses then take out common factor of both terms as shown below

$\begin{array}{c}\left(3-5\right)x+4y=-2x+4y\\ =-2\left(x-2y\right)\end{array}$