Watch out
Reversing the sign after adding a negative rather than dividing by one.
Scottish National 5 Mathematics
National 5 Maths Linear equations and inequations
Solve multi-step linear equations and inequations with rational coefficients and solutions.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Expand brackets and clear simple fractions where helpful.
- Be ready to work exactly without a calculator and show each mathematical step.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Linear equations and inequations is an assessed part of Scottish National 5 Mathematics in the algebra area. Solve multi-step linear equations and inequations with rational coefficients and solutions.
Expand brackets and clear simple fractions where helpful.
Collect unknown terms on one side and constants on the other.
Reverse the inequality only when multiplying or dividing by a negative.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- Multiplying or dividing an inequality by a negative reverses its sign.
Check
Expand, factorise or substitute back into the original expression to verify the result.
Exam tip
Keep equations aligned line by line so method marks remain visible, especially through sign and bracket changes.
Worked examples
Worked example 1
Linear equations and inequations worked example
Solve −3x + 5 ≤ 17.
- -3x ≤ 12
- Divide by −3 and reverse the sign.
Answer: x ≥ −4
Watch out
- Reversing the sign after adding a negative rather than dividing by one.
- Clearing denominators inconsistently.