Q49. - Algebra 2

Question

Simplify each expression

$7a+3b-4a-5b$

Step-by-Step Solution

Answer

$7a+3b-4a-5b$ is simplified to $3a-2b$

Step 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	$a+b=b+a$	$a·b=b·a$
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	$a\left(b+c\right)=ab+ac\text{ and }\left(b+c\right)a=ba+ca$

Step 2 - Simplify by grouping same variables

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

$\begin{array}{c}7a+3b-4a-5b=7a-4a+3b-5b\\ =\left(7-4\right)a+\left(3-5\right)b\end{array}$

Step 3 - Simplify

To simplify $\left(7-4\right)a+\left(3-5\right)b$, evaluate parentheses terms as shown below

$\left(7-4\right)a+\left(3-5\right)b=3a-2b$