Checking solutions by substitution | Year 7

01 / LEARN

The idea, step by step

A solution has to work in the original equation

Solving gives a candidate value. Checking means placing that value back into the equation exactly as it was first written. Calculate the left and right sides separately. The value is a solution only when those totals match.

In $3 x + 2 = 17$ , checking $x = 5$ means calculating $3 \times 5 + 2$ . The multiplication happens before the addition, so the left side is 17. The right side is also 17, so the check succeeds.

Check carefully, not just by guessing

Use brackets when you replace a variable in a longer expression. For example, with $n = 4$ , the expression $2 (n + 3)$ becomes $2 (4 + 3)$ , not $2 \times 4 + 3$ . Brackets are part of the rule.

A failed check is useful evidence. It tells you to look again at the equation or your calculations. Write both unequal totals so that the reason for rejecting the candidate is clear. Do not change the equation to make your answer fit.

A common trap

If a value looks close to the answer, it can count as a solution.

Instead: For these exact-number equations, equality must be exact. A left side of 7 does not satisfy a right side of 8.

02 / WORKED EXAMPLES

See the thinking

Example 1

Confirm a candidate

Does $x = 6$ solve $4 x - 5 = 19$ ?

Substitute 6 on the left: $4 \times 6 - 5$ .
Calculate multiplication first: $24 - 5 = 19$ .
The right side is 19.
The two sides match.

Yes,

x = 6

is a solution.

Example 2

Reject a plausible-looking value

Does $n = 8$ solve $n \div 2 + 3 = 8$ ?

Substitute 8: $8 \div 2 + 3$ .
Calculate the left side: $4 + 3 = 7$ .
The right side is 8, and $7 \neq 8$ .
So 8 is not a solution.

No; the left side is 7, not 8.

Check your understanding

Does $p = 7$ solve $2 p + 4 = 18$ ?

Show answer

Yes.

$2 \times 7 + 4 = 14 + 4 = 18$ , which equals the right side.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Check whether $x = 9$ solves $x + 8 = 17$ .
2 marks
Check whether $m = 4$ solves $5 m = 25$ .
2 marks
Check whether $a = 6$ solves $3 (a + 2) = 24$ .
2 marks
Check whether $n = 12$ solves $n \div 4 + 2 = 5$ .
2 marks
Which of 3, 4 and 5 solves $4 t - 3 = 13$ ? Show the successful check.
3 marks
A student says $b = 5$ solves $2 (b + 4) = 14$ because $2 \times 5 + 4 = 14$ . Explain the error and check $b = 3$ .
3 marks

Read the worked solutions

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

Check whether $x = 9$ solves $x + 8 = 17$ .
2 marks
Substitute 9: $9 + 8 = 17$ .
Both sides are 17.
Yes.
Check whether $m = 4$ solves $5 m = 25$ .
2 marks
$5 \times 4 = 20$ .
$20 \neq 25$ , so 4 does not work.
No.
Check whether $a = 6$ solves $3 (a + 2) = 24$ .
2 marks
$3 (6 + 2) = 3 \times 8 = 24$ .
The brackets are calculated before multiplication.
Yes.
Check whether $n = 12$ solves $n \div 4 + 2 = 5$ .
2 marks
$12 \div 4 + 2 = 3 + 2 = 5$ .
Both sides are 5.
Yes.
Which of 3, 4 and 5 solves $4 t - 3 = 13$ ? Show the successful check.
3 marks
For 3, $4 \times 3 - 3 = 9$ .
For 4, $4 \times 4 - 3 = 13$ .
For 5, $4 \times 5 - 3 = 17$ .
Only 4 produces 13.
$t = 4$
A student says $b = 5$ solves $2 (b + 4) = 14$ because $2 \times 5 + 4 = 14$ . Explain the error and check $b = 3$ .
3 marks
With $b = 5$ , the left side is $2 (5 + 4) = 18$ , not 14.
With $b = 3$ , $2 (3 + 4) = 2 \times 7 = 14$ .
The brackets were ignored; $b = 3$ works.

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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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