YEAR 7 · LINEAR EQUATIONS · 15 MIN

One-step addition/subtraction equations

Undo one addition or subtraction to find the unknown, and show the same operation on each side.

In this lesson

Solve an equation involving one addition
Solve an equation involving one subtraction
Check the result by substitution

Before you start

Equality and balancing
Addition and subtraction facts

01 / LEARN

Understand the idea.

Undo addition by subtraction

An inverse operation undoes another operation. If $7$ has been added to the unknown in $x + 7 = 20$ , subtract $7$ from both sides to recover its starting value: $x = 13$ .

The aim is to leave the variable alone while preserving equality. Write the subtraction on both sides before simplifying. Then check the result by putting it into the original equation; here $13 + 7 = 20$ .

Undo subtraction by addition

If an amount was subtracted from the unknown, add it back. In $n - 6 = 15$ , the $15$ is what remains after removing $6$ , so the original amount is $15 + 6 = 21$ .

Choose the inverse from the operation attached to the variable. The equations $n + 6 = 15$ and $n - 6 = 15$ need different inverse operations, even though they contain the same numbers. Check against the equation you were actually given.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Undo an addition

Solve $a + 12 = 31$ .

Worked solution

1
Undo the addition on both sides.
$a + 12 - 12 = 31 - 12$
Subtraction reverses adding 12 without changing the balance.
2
Calculate the missing value.
$a = 19$
There must be 19 before 12 is added to make 31.
3
Substitute into the original equation.
$19 + 12 = 31$
The equality confirms the value.

Answer

$a = 19$

EXAMPLE 02

Recover a starting amount

After 9 counters are removed, $c - 9 = 16$ . Find $c$ .

Worked solution

1
Add back the removed counters on both sides.
$c - 9 + 9 = 16 + 9$
The starting collection is the remainder plus the 9 removed.
2
Calculate the starting collection.
$c = 25$
Adding 9 undoes the subtraction from c.
3
Check by removing 9 again.
$25 - 9 = 16$
Starting with 25 counters leaves the stated 16 counters.

Answer

$c = 25$

03 / YOUR TURN

Try it yourself.

Check your understanding

Solve $r - 11 = 18$ .

Show answer & reasoning

$r = 29$ .

Add $11$ to both sides because this undoes subtracting $11$ . Then $r = 18 + 11 = 29$ , and $29 - 11 = 18$ verifies the result.

Keep practising

6 worksheet questions · 14 marks

Open worksheet Worked solutions

Read the questions online

Solve $x + 5 = 17$ .
2 marks
Solve $p - 7 = 14$ .
2 marks
Solve $a + 18 = 45$ .
2 marks
Solve $n - 26 = 19$ .
2 marks
A box holds $b$ pencils. Adding 8 pencils gives 30 pencils. Write and solve an equation.
3 marks
Noah had $s$ stickers. He gave away 13 and has 24 left. Find $s$ using an equation.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Solve $x + 5 = 17$ .
2 marks
Subtract 5 from both sides.
$x = 17 - 5 = 12$ .
Check: $12 + 5 = 17$ .
$x = 12$
Solve $p - 7 = 14$ .
2 marks
Add 7 to both sides.
$p = 14 + 7 = 21$ .
Check: $21 - 7 = 14$ .
$p = 21$
Solve $a + 18 = 45$ .
2 marks
Subtract 18 from both sides.
$a = 45 - 18 = 27$ .
Check: $27 + 18 = 45$ .
$a = 27$
Solve $n - 26 = 19$ .
2 marks
Add 26 to both sides.
$n = 19 + 26 = 45$ .
Check: $45 - 26 = 19$ .
$n = 45$
A box holds $b$ pencils. Adding 8 pencils gives 30 pencils. Write and solve an equation.
3 marks
The starting number plus 8 equals 30.
Subtract 8 from both sides: $b = 30 - 8 = 22$ .
Check: $22 + 8 = 30$ .
$b + 8 = 30$ ; $b = 22$ pencils.
Noah had $s$ stickers. He gave away 13 and has 24 left. Find $s$ using an equation.
3 marks
Add 13 to both sides of $s - 13 = 24$ .
$s = 24 + 13 = 37$ .
Check: $37 - 13 = 24$ .
$s - 13 = 24$ ; $s = 37$ stickers.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Year 7 linear equations with natural-number solutions: equality, inverse operations, substitution checks and familiar models. Formal variables-on-both-sides techniques are not required here.

Official curriculum source ↗

In this lesson

Understand the idea.

Undo addition by subtraction

Undo subtraction by addition

See the method in action.

Undo an addition

Undo the addition on both sides.

Calculate the missing value.

Substitute into the original equation.

Recover a starting amount

Add back the removed counters on both sides.

Calculate the starting collection.

Check by removing 9 again.

Try it yourself.

Check your understanding

Keep practising