Solve One-Step Addition and Subtraction Equations

Students solve equations of the form x + p = q and x - p = q by using inverse operations, undoing addition with subtraction and vice versa. They show their work as a balanced equation and verify their solution by substitution.

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Grade 6 · Equations and Inequalities · question 1 of 3

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x + 3 = 14, x =

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An equation stays balanced on both sides.

An inverse operation undoes the one that is there.

That isolates the variable.

Read it: Undo it on both sides

x + 9 = 15 is a tape of 15 cut into x and 9. Take the 9 away and x is what is left: 15 − 9 = 6.

Draw the tape: the whole on top, x and the other part below.
Undo what was done to x, on both sides: + 9 is undone by − 9.
Work it out and check: 15 − 9 = 6, and 6 + 9 = 15.

An equation is a balance: doing the same to both sides keeps it true.

Each operation has its undo: add and take away undo each other, and so do times and divide.

The check puts the answer back: if 6 + 9 makes 15, then x = 6 is right.

To find x, undo what was done to it, the same on both sides, then check.

Adding 9 instead of taking it away, and writing x = 24.

x + 9 = 15 means x is 9 less than 15: x = 15 − 9 = 6.

x + 13 = 17, x = ___ — 4. 17 − 13 = 4. Check: 4 + 13 = 17.

x + 7 = 15

An equation is like a balanced scale — both sides must stay equal.

Here's our equation: x plus seven equals fifteen.

Our goal is to get x all by itself on one side.

What's the opposite of adding seven?

Subtracting seven! That's called the inverse operation.

We subtract seven from BOTH sides to keep the equation balanced.

On the left, plus seven minus seven cancels out, leaving just x.

On the right, fifteen minus seven equals eight.

So x equals eight!

Let's check. Put eight back in for x in the original equation.

Eight plus seven equals fifteen. It works!

x equals eight. Nice work!

Grade 6 · Using inverse operations to isolate x

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

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MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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