Substitution checks | Year 8

01 / LEARN

The idea, step by step

A check is independent evidence

Substitute the proposed number into the left-hand side and the right-hand side separately. Only matching results show that the number is a solution.

Checking one value does not by itself solve the whole equation. A failed check rejects that value but does not identify the correct replacement.

Return to the original equation

Checking only the final line x = 4 simply repeats your answer. An earlier rearrangement may contain the error, so use the original question.

Put negative substitutions in brackets. Respect the grouping of a numerator and the usual order of operations.

A common trap

Checking only the statement x = 4.

Instead: Evaluate each side of the original equation instead.

02 / WORKED EXAMPLES

See the thinking

Example 1

Confirm a negative value

Does $x = - 2$ solve $3 x + 7 = 1$ ?

Left: $3 (- 2) + 7 = - 6 + 7 = 1$ .
Right: 1.
The equal results confirm the value.

Yes; both sides are 1.

Example 2

Reject a guess

Does $x = 4$ solve $2 (x + 3) = 3 x$ ?

Left: $2 (4 + 3) = 14$ .
Right: $3 (4) = 12$ .
The original equation is false for x = 4.

No; 14 is not 12.

Check your understanding

Does $x = 3$ solve $4 x - 5 = 7$ ?

Show answer

Yes.

The left side is $12 - 5 = 7$ , equal to the right.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Check x = 5 in $2 x + 3 = 13$ .
2 marks
Check x = -1 in $4 x + 2 = - 2$ .
2 marks
Check x = 2 in $3 (x + 1) = 8$ .
2 marks
Check $x = 3 / 2$ in $4 x - 1 = 5$ .
2 marks
A student gets x = 5 for $5 x + 4 = 24$ . Check the guess and find the correct solution.
3 marks
Which of x = -2, 0 and 2 solves $3 x + 2 = x - 2$ ? Show the checks.
3 marks

Read the worked solutions

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

Check x = 5 in $2 x + 3 = 13$ .
2 marks
The left side is $10 + 3 = 13$ .
It equals the right side.
It is a solution.
Check x = -1 in $4 x + 2 = - 2$ .
2 marks
The left side is $- 4 + 2 = - 2$ .
Both values agree.
It is a solution.
Check x = 2 in $3 (x + 1) = 8$ .
2 marks
The left side is $3 (3) = 9$ .
Nine is not eight.
It is not a solution.
Check $x = 3 / 2$ in $4 x - 1 = 5$ .
2 marks
The left side is $6 - 1 = 5$ .
It equals the right side.
It is a solution.
A student gets x = 5 for $5 x + 4 = 24$ . Check the guess and find the correct solution.
3 marks
At 5 the left side is 29, so the guess fails.
Subtract 4 and divide by 5; $5 (4) + 4 = 24$ .
$x = 4$ .
Which of x = -2, 0 and 2 solves $3 x + 2 = x - 2$ ? Show the checks.
3 marks
At -2, the two sides are -4 and -4.
At 0 they are 2 and -2; at 2 they are 8 and 0.
Only x = -2.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics (2026)

Multi-step equations; brackets and variables on both sides; equations with rational solutions; substitution checks; one-variable inequalities and number-line solutions; tables and straight-line graphs; horizontal/vertical lines; how coefficients change a graph; graphical solutions and intersection checks; real-world linear models with digital exploration.

Official curriculum source ↗

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