MINI LESSON
Identifying Properties
Properties of equality justify the steps used to transform equations.
When the same quantity is added to both sides of an equation, the addition property of equality is used.
When the same quantity is subtracted from both sides of an equation, the subtraction property of equality is used.
A correct justification explains why one equation is equivalent to the next.
Question 1
When solving the equation \(4x^2-16=0\), Laura wrote \(4x^2=16\) as her first step. Which property justifies Laura's first step?
Question 2
Stephanie is solving the equation \(x^2-12=7x-8\). Her first step is shown below.
Given: \(x^2-12=7x-8\)
Step 1: \(x^2-4=7x\)
Which property justifies her first step?
Question 3
Chloe is solving the equation \(x^2+5x=3x+3\). Her first step is shown below.
Given: \(x^2+5x=3x+3\)
Step 1: \(x^2+2x-3=0\)
Which property justifies this step?
Question 4
When solving \(x^2+6x=-8\) for \(x\), a student wrote \(x^2+6x+8=0\) as their first step. Which property justifies this step?