Q13.

Question

Simplify each expression

$3 x + 4 y - 5 x$

Step-by-Step Solution

Verified

Answer

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

1Step 1 - 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	$a + b = b + a$	$a \cdot b = b \cdot a$
Associative	$(a + b) + c = a + (b + c)$	$(a \cdot b) \cdot c = a \cdot (b \cdot c)$
Identity	$a + 0 = a = 0 + a$	$a \cdot 1 = a = 1 \cdot a$
Inverse	$a + (- a) = 0 = (- a) + a$	If $a \neq 0$ , then $a \cdot \frac{1}{a} = 1 = \frac{1}{a} \cdot a$
Distributive	$a (b + c) = a b + a c and (b + c) a = b a + c a$

2Step 2 - 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

$\begin{matrix} 3 x + 4 y - 5 x = 3 x - 5 x + 4 y \\ = (3 - 5) x + 4 y \end{matrix}$