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All courses Math Foundations · MF.EQ.5 32 of 60
Solve one-step equations and interpret the solution in context.

Undo addition or subtraction in one step

Problem
Solve the equation: x + 7 = 12. What is x?
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Hint

Look at the operation on x. Since 7 is added to x, start by subtracting 7 from both sides.

Use inverse operations: subtraction undoes addition and keeps the equation balanced when you do it to both sides.

Solution walkthrough

01

Notice what is happening to x

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

The variable x has 7 added to it. To solve for x, we undo that addition with the inverse operation, subtraction.

02

Subtract 7 from both sides

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

Subtracting the same number from both sides keeps the equation balanced and removes the +7 attached to x.

03

Simplify the equation

\[x~=~5\]

On the left, +7 and -7 cancel. On the right, 12 - 7 = 5, so x must be 5.

04

Check and state the answer

\[5~+~7~=~12,~\text{so}~x~=~5\]

Substituting 5 back into the original equation gives a true statement, so 5 is the correct value of x.

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Another way

  1. Think backward from 12: what number plus 7 equals 12? That number is 5.

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Common mistake

A common mistake is to add 7 to 12 and say x = 19. Since 7 was added to x, you must subtract 7 to undo it.