Substitution checks | Year 8

01 / LEARN

Understand the idea.

A check is independent evidence

To check a proposed solution, substitute it into the original left and right sides separately. An equation is true for that value only when the two calculations produce the same result.

A successful check confirms the proposed value, while a failed check rejects it. Neither calculation by itself explains how to find another solution, or proves that no other solution exists.

Return to the original equation

Use the original equation rather than the final rearranged line. An incorrect algebra step might lead to $x = 4$ ; checking only that final statement repeats the guess instead of testing the original relationship.

Put negative substitutions in brackets: $3 (- 2)$ means three times negative two. Work inside brackets first, then multiply, then add or subtract. Keep grouped numerators together when substituting into fractions.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Confirm a negative value

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

Worked solution

1
Evaluate the original left side.
$3 (- 2) + 7 = - 6 + 7 = 1$
Brackets keep the negative substitution attached to its multiplication.
2
Evaluate the original right side.
$RHS = 1$
The right side is a constant and is unchanged by substitution.
3
Compare the two values.
$LHS = RHS = 1$
The equality is true, so $x = - 2$ is a solution.

Answer

Yes; both sides are 1.

EXAMPLE 02

Reject a guess

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

Worked solution

1
Substitute into the left side.
$2 (4 + 3) = 2 (7) = 14$
The addition inside the bracket comes before multiplication.
2
Substitute into the right side.
$3 (4) = 12$
Both sides must be evaluated using the same proposed value.
3
Compare and reject the guess.
$14 \neq 12$
The original equality is false at $x = 4$ , so this value is not a solution.

Answer

No; 14 is not 12.

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

Yes.

At $x = 3$ , the original left side is $4 (3) - 5 = 12 - 5 = 7$ . This equals the original right side, so the proposed value is a solution.

Keep practising

6 worksheet questions · 14 marks

Open worksheet 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 $x = \frac{3}{2}$ 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 $x = - 2, 0, 2$ 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 $x = \frac{3}{2}$ 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 $x = - 2, 0, 2$ 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 ↗

In this lesson

Understand the idea.

A check is independent evidence

Return to the original equation

See the method in action.

Confirm a negative value

Evaluate the original left side.

Evaluate the original right side.

Compare the two values.

Reject a guess

Substitute into the left side.

Substitute into the right side.

Compare and reject the guess.

Try it yourself.

Check your understanding

Keep practising