Secondary 4 equation solving becomes more reliable when students stop thinking of terms as “moving across” and start preserving equality. This Mathematics tuition guide for Punggol families explains linear equations, brackets, fractions, variables on both sides and denominator control through original worked examples.
A student may solve 3x + 5 = 17 confidently but lose control when fractions or brackets appear. Another may get the right answer through an invalid sign change. The aim is not only to reach x. It is to make every line equivalent to the one before it.
At eduKatePunggol, Secondary 4 Mathematics is taught in focused groups of up to three students in 1.5-hour lessons near Punggol MRT. This guide supports the wider Secondary 4 Mathematics year plan. The examples below are original teaching examples.
An equation is a statement of equality
If we perform the same valid operation on both sides, equality is preserved.
From:
3x + 5 = 17
subtract 5 from both sides:
3x = 12.
Then divide both sides by 3:
x = 4.
Worked example 1: variables on both sides
Solve 5x − 7 = 2x + 11.
Subtract 2x from both sides:
3x − 7 = 11.
Add 7:
3x = 18.
Therefore x = 6.
Check: both original sides equal 23 when x = 6.
Brackets should be simplified before unnecessary movement
Solve 3(2x − 5) = 4x + 7.
Expand:
6x − 15 = 4x + 7.
Then:
2x − 15 = 7
2x = 22
x = 11.
If the expansion step fails, the equation topic is not necessarily the main weakness. Use the expansion and factorisation guide to repair the earlier dependency.
Fractions become easier when denominators are cleared carefully
Solve x/3 + 2 = 7.
x/3 = 5, so x = 15.
For more complicated fractional equations, multiply the whole equation by a common denominator, not only the term you want to remove.
Worked example 2: clear two denominators
Solve x/4 + (x − 1)/6 = 3.
The least common multiple of 4 and 6 is 12. Multiply every term by 12:
3x + 2(x − 1) = 36.
Then:
3x + 2x − 2 = 36
5x = 38
x = 38/5.
A common error is to multiply the first two fractions by 12 but forget the 3 on the right-hand side.
Worked example 3: denominator containing the variable
Solve 3/(x + 1) = 1.
First note that x ≠ −1.
For allowed x, multiply both sides by x + 1:
3 = x + 1, so x = 2.
Check the original denominator: 2 + 1 ≠ 0, so the solution is permitted.
This connects to the algebraic-fractions guide, where restrictions must also be preserved.
Worked example 4: a linear word problem
An invented example: three identical notebooks and a $4 pen cost $25. Let x be the price of one notebook.
The equation is:
3x + 4 = 25.
So 3x = 21 and x = 7.
The notebook costs $7.
The modelling step—defining x and building the equation—comes before the algebra.
Check solutions by substitution
Substituting the final value into the original equation catches many sign and denominator mistakes.
For x = 11 in 3(2x − 5) = 4x + 7:
left side = 3(22 − 5) = 51.
right side = 44 + 7 = 51.
The equality is restored.
How we diagnose equation-solving mistakes
Equality error: an operation is applied to only one side.
Expansion error: a bracket is simplified incorrectly.
Fraction error: the common denominator does not multiply every term.
Restriction error: a denominator condition is ignored.
Modelling error: the word problem is converted into the wrong equation before solving begins.
Why the three-student format helps
In a group of up to three students, the tutor can ask one learner to explain the operation, another to perform it and another to check the solution in the original equation. This makes equality visible rather than reducing the lesson to symbol movement.
What a 90-minute lesson could look like
An illustrative lesson could use ten minutes for inverse-operation retrieval, twenty minutes for variables on both sides and brackets, twenty minutes for fractional equations, twenty minutes for worded models and twenty minutes for independent work, checking, error review and continuation practice.
Repair, stabilisation and extension
Repair: use one-step and two-step equations with clean integer coefficients.
Stabilisation: mix brackets, variables on both sides and simple fractions so the student must choose the next operation independently.
Extension: include fractional expressions, modelling and equations requiring careful domain restrictions.
Try a short independent set
- Solve 7x − 5 = 23.
- Solve 4x + 3 = 2x + 15.
- Solve x/5 + 2 = 8.
Answers: x = 4; x = 6; and x = 30.
What progress should look like
- operations preserve equality;
- brackets are expanded accurately;
- variables on both sides are collected cleanly;
- common denominators reach every term;
- denominator restrictions are retained;
- solutions are checked by substitution.
Punggol class details and consultation inputs
eduKatePunggol Secondary Mathematics tutorials run for 1.5 hours in groups of up to three students near Punggol MRT. Confirm current class availability, fees and meeting arrangements directly.
Bring the student’s subject level, examination year and recent equations with the original steps visible. The first invalid line often tells us more than the final wrong answer.
Frequently asked questions
Can I move a term across and change its sign?
That shortcut can describe the result, but the underlying reason is that the same addition or subtraction was performed on both sides.
Why check the answer?
Substitution tests whether the final value really satisfies the original equation and can expose earlier sign or fraction errors.
Preserve equality from the first line to the last
Return to the Secondary 4 Mathematics year plan for the wider SEC runway. For equations involving two variables, use the simultaneous-equations guide.
Keep both sides balanced, clear denominators carefully and check the original equation. Families can WhatsApp eduKatePunggol with recent school work to discuss a suitable next step.
