One-step addition/subtraction equations | Year 7

01 / LEARN

The idea, step by step

Undo addition by subtraction

Addition and subtraction undo one another. If $x + 7 = 20$ , the unknown has had 7 added to it. To find its starting value, subtract 7 from each side: $x = 20 - 7 = 13$ .

Write what you do to both sides, even when you can see the answer mentally. This makes your reasoning easy to follow and helps when equations become longer. Finish by substituting the value into the original equation.

Undo subtraction by addition

If $n - 6 = 15$ , six has been taken away from the unknown. Add 6 to both sides to recover the starting value: $n = 15 + 6 = 21$ . The check is $21 - 6 = 15$ .

Read the operation attached to the variable before choosing its inverse. The equation $n - 6 = 15$ does not mean that 6 should be subtracted from 15. Your aim is to undo the operation on $n$ , while keeping the two sides equal.

A common trap

Always subtract the visible number, whatever the equation says.

Instead: Use the inverse of the operation on the variable. Subtract after addition; add after subtraction.

02 / WORKED EXAMPLES

See the thinking

Example 1

Undo an addition

Solve $a + 12 = 31$ .

Subtract 12 from both sides.
$a = 31 - 12 = 19$ .
Check in the original equation: $19 + 12 = 31$ .

a = 19

Example 2

Recover a starting amount

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

Add 9 to both sides.
$c = 16 + 9 = 25$ .
Check: $25 - 9 = 16$ .
The starting collection contained 25 counters.

c = 25

Check your understanding

Solve $r - 11 = 18$ .

Show answer

$r = 29$ .

Add 11 to both sides: $r = 18 + 11 = 29$ . The check is $29 - 11 = 18$ .

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF 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 ↗

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