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All courses Algebra I · A-REI.1 5 of 76
Explain equation-solving steps as logical consequences of equality and justify solution methods.

Name the equality property used in a solving step

Problem
In the step from \(x~+~7~=~12\) to \(x~=~5\), identify the property of equality used.
Your answer
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Hint

Ask what operation was undone. The equation changes from x + 7 = 12 to x = 5 by removing 7 from both sides.

When the same number is subtracted from both sides of an equation, that uses the subtraction property of equality.

Solution walkthrough

01

Compare the two equation states

\[\text{before}:~x+7=12;~\text{after}:~x=5\]

The added 7 disappears from the variable side, while 12 decreases to 5. Identify the operation that creates both changes.

02

Make the balancing operation explicit

\[x+7-7=12-7\]

Subtracting the same value from both sides preserves equality. On the left it undoes +7; on the right it produces 5.

03

Simplify and verify the result

\[x=5;~\text{check}:~5+7=12\]

The balanced subtraction yields the stated next line, and substituting 5 satisfies the original equation.

04

Name the equality property

\[\text{subtraction}~\text{property}~\text{of}~\text{equality}\]

Because 7 was subtracted from both sides, the exact justification is the subtraction property of equality, choice A.

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Another way

  1. Use the balance-scale interpretation: removing seven equal units from each side keeps the two sides balanced; that is subtraction on both sides.

!

Common mistake

Do not name the addition property merely because the original equation contains +7. The property is named for the operation performed to move to the next line.

Solution walkthrough video