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All courses Math I · A-REI.1 5 of 59
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.
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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

Look at the original equation

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

The variable x has 7 added to it in the original equation.

02

Identify the inverse operation

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

To undo adding 7, subtract 7 from each side while keeping the equation balanced.

03

See the resulting equation

\[x~=~5\]

After subtracting 7 from both sides, the equation simplifies to x = 5.

04

Name the property

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

Because the same value was subtracted from both sides, the property used is the subtraction property of equality.

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Another way

  1. You can focus on the word “both sides.” Any time the same number is subtracted from each side to keep the equation balanced, that is the subtraction property of equality.

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Common mistake

A common mistake is to say division property of equality because the final answer is smaller. The key is not the size change, but the operation actually used on both sides.