Introduction to Modeling: Background You’ll Need 2

Lumen Learning

Introduction to Modeling: Background You’ll Need 2

Solve equations by subtracting

Solve Equations Using the Subtraction Property of Equality

Our puzzle has given us an idea of what we need to do to solve an equation. The goal is to isolate the variable by itself on one side of the equation. In the previous examples, we used the Subtraction Property of Equality, which states that when we subtract the same quantity from both sides of an equation, we still have equality.

subtraction property of equality

For any numbers [latex]a,b[/latex], and [latex]c[/latex], if [latex]a=b[/latex], then [latex]a-c=b-c[/latex]

Think about twin brothers Andy and Bobby. They are [latex]17[/latex] years old. How old was Andy [latex]3[/latex] years ago? He was [latex]3[/latex] years less than [latex]17[/latex], so his age was [latex]17 - 3[/latex], or [latex]14[/latex]. What about Bobby’s age [latex]3[/latex] years ago? Of course, he was [latex]14[/latex] also. Their ages are equal now, and subtracting the same quantity from both of them resulted in equal ages [latex]3[/latex] years ago.

[latex]\begin{array}{c}a=b\\ a - 3=b - 3\end{array}[/latex]

How To: Solve an Equation Using the Subtraction Property of Equality

Use the Subtraction Property of Equality to isolate the variable.
Simplify the expressions on both sides of the equation.
Check the solution.

Solve: [latex]x+8=17[/latex].

Solve: [latex]100=y+74[/latex].

	[latex]x+8=17[/latex]
Subtract [latex]8[/latex] from both sides.	[latex]x+8\color{red}{-8}\color{black}=17\color{red}{-8}[/latex]
Simplify.	[latex]x=9[/latex]
	[latex]x+8=17[/latex]
	[latex]\color{red}{9}\color{black}+8=17[/latex]
	[latex]17=17\quad\checkmark[/latex]

	[latex]100=y+74[/latex]
Subtract [latex]74[/latex] from both sides.	[latex]100\color{red}{-74}\color{black}=y+74\color{red}{-74}[/latex]
Simplify.	[latex]26=y[/latex]
Substitute [latex]26[/latex] for [latex]y[/latex] to check.	[latex]100=y+74[/latex] [latex]100=\color{red}{26}\color{black}+74[/latex] [latex]100=100\quad\checkmark[/latex]