Equality and balancing | Year 7

01 / LEARN

The idea, step by step

An equation compares two totals

The equals sign means that the value on its left is exactly the same as the value on its right. It does not mean that an answer must come next. For example, $8 + 4 = 7 + 5$ is true because both sides equal 12.

A variable can stand for a missing value. In $x + 3 = 8$ , the left total must be 8, so the value of $x$ is 5. This value of $x$ is called a solution.

Keep both sides equal

Think of an equation as balanced pans. Removing 3 units from both pans leaves equal totals. Written mathematically, $x + 3 - 3 = 8 - 3$ , so $x = 5$ . Removing 3 from only one side would destroy the equality.

You may add or subtract the same amount on both sides. You may also multiply or divide both sides by the same non-zero number. Choose a change that makes the unknown easier to see, and write the resulting equation on a new line.

A common trap

Changing one side is enough if the other side already looks simple.

Instead: Every change used to preserve equality must affect both sides in the same way. A simple-looking equation can still be false.

02 / WORKED EXAMPLES

See the thinking

Example 1

Find the missing amount

Find $x$ in $x + 6 = 14$ .

Both sides must have the same total.
Subtract 6 from both sides: $x + 6 - 6 = 14 - 6$ .
This leaves $x = 8$ .
Check the total: $8 + 6 = 14$ .

x = 8

Example 2

Two expressions can be equal

Complete $9 + 7 = n + 10$ .

The left side has value $9 + 7 = 16$ .
The right side must therefore equal 16.
The number added to 10 to make 16 is 6.
Check: $9 + 7 = 16$ and $6 + 10 = 16$ .

n = 6

Check your understanding

In $p + 4 = 13$ , what should be subtracted from both sides, and what is $p$ ?

Show answer

Subtract 4; $p = 9$ .

Subtracting the same 4 from each equal total leaves $p = 13 - 4 = 9$ .

03 / WORKSHEET

Your turn

6 questions · 11 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Complete $7 + 8 = 10 + □$ .
1 mark
Is $18 - 5 = 6 + 7$ true? Explain.
2 marks
Find $x$ in $x + 3 = 11$ by keeping both sides balanced.
2 marks
An equation is $m - 5 = 9$ . Explain why adding 5 to both sides is useful.
2 marks
A student changes $a + 7 = 19$ into $a = 19$ . What change has been missed?
2 marks
The same number is added to both sides of a true equation. Must the new equation be true? Explain with an example.
2 marks

Read the worked solutions

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

Complete $7 + 8 = 10 + □$ .
1 mark
The left total is 15.
The missing value is $15 - 10 = 5$ .
5
Is $18 - 5 = 6 + 7$ true? Explain.
2 marks
$18 - 5 = 13$ and $6 + 7 = 13$ .
The expressions have equal values.
Yes; each side is 13.
Find $x$ in $x + 3 = 11$ by keeping both sides balanced.
2 marks
Subtract 3 from both sides.
$x = 11 - 3 = 8$ .
$x = 8$
An equation is $m - 5 = 9$ . Explain why adding 5 to both sides is useful.
2 marks
Adding 5 undoes subtracting 5 on the left.
$m - 5 + 5 = 9 + 5$ , so $m = 14$ .
$m = 14$
A student changes $a + 7 = 19$ into $a = 19$ . What change has been missed?
2 marks
Removing 7 on the left must also remove 7 on the right.
The balanced result is $a = 19 - 7 = 12$ .
Subtracting 7 from the right side.
The same number is added to both sides of a true equation. Must the new equation be true? Explain with an example.
2 marks
Equal starting totals remain equal after the same addition.
For example, $6 = 6$ becomes $6 + 4 = 6 + 4$ , and both sides are 10.
Yes.

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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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