Equality and balancing | Year 7

01 / LEARN

Understand the idea.

An equation compares two totals

An equation says that two expressions have the same value. In $8 + 4 = 7 + 5$ , both sides equal $12$ . Read the equals sign as “has the same value as”, even when there are calculations on both sides.

A solution is a value that makes an equation true. In $x + 3 = 8$ , the unknown must be $5$ : adding $3$ to it produces the required total of $8$ .

Keep both sides equal

Think of the two sides as balanced pans. Removing $3$ counters from each pan preserves the balance. That is why $x + 3 = 8$ becomes $x = 5$ when we subtract $3$ from both sides.

Choose an operation that leaves the unknown on its own. Adding or subtracting the same amount preserves equality; multiplying or dividing both sides by the same non-zero number also preserves the solutions. Record each new equation on a fresh line.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Find the missing amount

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

Worked solution

1
Subtract 6 from both sides.
$x + 6 - 6 = 14 - 6$
Removing the same amount from equal totals keeps them equal.
2
Simplify each side.
$x = 8$
The added 6 and subtracted 6 cancel.
3
Check the original total.
$8 + 6 = 14$
The left side equals the original right side, so 8 is a solution.

Answer

$x = 8$

EXAMPLE 02

Two expressions can be equal

Complete $9 + 7 = n + 10$ .

Worked solution

1
Calculate the left total.
$9 + 7 = 16$
The equals sign requires the right expression to have this same value.
2
Write the required right total.
$n + 10 = 16$
The unknown and 10 together must make 16.
3
Subtract 10 from both sides.
$\begin{aligned} n + 10 - 10 & = 16 - 10 \\ n & = 6 \end{aligned}$
Subtracting 10 isolates the missing addend.
4
Compare both original expressions.
$\begin{aligned} 9 + 7 & = 16 \\ 6 + 10 & = 16 \end{aligned}$
Both sides give 16 when the missing number is 6.

Answer

$n = 6$

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

Subtract 4; $p = 9$ .

Subtract $4$ from both sides to undo the addition: $p = 13 - 4 = 9$ . Substituting gives $9 + 4 = 13$ , so the original equality holds.

Keep practising

6 worksheet questions · 11 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

An equation compares two totals

Keep both sides equal

See the method in action.

Find the missing amount

Subtract 6 from both sides.

Simplify each side.

Check the original total.

Two expressions can be equal

Calculate the left total.

Write the required right total.

Subtract 10 from both sides.

Compare both original expressions.

Try it yourself.

Check your understanding

Keep practising