Sec 2 Linear Equations Worked Examples for 2026/2027 (Singapore MOE Syllabus) — Step-by-Step Worked Examples

Quick answer

Ever find your heart sinking when you see a linear equation that doesn't look like what you've practiced? You're not alone. Most students know the basics but freeze when the question looks different. After reading this, you'll know how to tackle these problems step by step and avoid losing marks.

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What you need to know

A linear equation is a math sentence with an equal sign, where the highest power of the variable (like 𝑥) is 1. It looks like ax + 𝑏 = 𝑐. Solving it means finding the value of 𝑥 that makes the equation true.

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Understanding Linear Equations

Key Concepts

Linear equations are like puzzles. You need to find the missing piece, which is the value of 𝑥. In simple terms, you'll rearrange the equation to isolate 𝑥 on one side.

Why Students Struggle

I've seen students panic because the questions in exams look different from tutorials. They rush through algebra steps and make careless errors. Remember, Singapore exams test how you apply concepts, not just how well you memorise them.

Quick check

Let's test what you've learned with a couple of questions. Answers are below.

1. Solve for 𝑥: 3𝑥 + 5 = 14.
2. Solve for 𝑥: 5𝑥 - 3 = 2𝑥 + 9.

Common mistakes students make

1. Rushing through steps: Don’t skip steps even if the equation looks simple. This is where many students lose unnecessary marks.
2. Overcomplicating: Sometimes students add extra steps that aren't needed. Simplify first.
3. Misplacing negatives: Keep track of negative signs. They can change your answer completely.

Exam tip

In exams, presentation matters. Line up your work neatly so you can easily spot errors. Always double-check your last step, especially if it’s a subtraction or involves negatives. This helps prevent careless mistakes.

Worked examples

Question

Solve for 𝑥: 2(𝑥 + 3) = 16

Solution

Step 1: Expand the brackets: 2(𝑥 + 3) = 2𝑥 + 6
Why: We need to remove the bracket before we can collect like terms — otherwise, the equation is still "locked".

Step 2: Subtract 6 from both sides: 2𝑥 + 6 - 6 = 16 - 6
Why: This isolates the 2𝑥 term on one side, making it easier to solve.

Step 3: Simplify: 2𝑥 = 10
Why: Now we have a simpler equation to solve.

Step 4: Divide both sides by 2: 𝑥 = 5
Why: Dividing by 2 gives us the value of 𝑥 directly.

Question

Solve for 𝑥: 4𝑥 - 7 = 2𝑥 + 9

Solution

Step 1: Move 2𝑥 to the left side: 4𝑥 - 2𝑥 - 7 = 9
Why: We want all the 𝑥 terms on one side to simplify the equation.

Step 2: Simplify: 2𝑥 - 7 = 9
Why: This gives us a clearer view of what 𝑥 is doing in the equation.

Step 3: Add 7 to both sides: 2𝑥 = 16
Why: Adding 7 helps isolate the 𝑥 term even further.

Step 4: Divide both sides by 2: 𝑥 = 8
Why: This step gives us the final answer for 𝑥.

Question

Solve for 𝑥: 5(𝑥 - 4) = 3𝑥 + 6

Solution

Step 1: Expand the brackets: 5(𝑥 - 4) = 5𝑥 - 20
Why: Expanding makes it easier to see all terms.

Step 2: Subtract 3𝑥 from both sides: 5𝑥 - 3𝑥 - 20 = 6
Why: We want to gather all 𝑥 terms on one side.

Step 3: Simplify: 2𝑥 - 20 = 6
Why: This makes the equation simpler.

Step 4: Add 20 to both sides: 2𝑥 = 26
Why: Isolating 2𝑥 helps us solve for 𝑥.

Step 5: Divide by 2: 𝑥 = 13
Why: Dividing gives us the final answer.

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Question

Solve for 𝑥: 3(𝑥 + 2) - 2(𝑥 - 1) = 4

Solution

Step 1: Expand the brackets: 3(𝑥 + 2) = 3𝑥 + 6 and 2(𝑥 - 1) = 2𝑥 - 2
Why: We need to see all terms clearly to proceed.

Step 2: Substitute back: 3𝑥 + 6 - 2𝑥 + 2 = 4
Why: This combines the terms into one equation.

Step 3: Simplify: 𝑥 + 8 = 4
Why: This shows the equation in its simplest form.

Step 4: Subtract 8 from both sides: 𝑥 = -4
Why: Isolating 𝑥 gives us the final answer.

Quick summary

• Linear equations are about finding 𝑥, where 𝑥 is the variable.
• Always remove brackets first.
• Move terms to isolate 𝑥 on one side.
• Simplifying each step prevents careless mistakes.
• Watch out for negative signs; they can change your answer.

FAQ

Q: What if I see a linear equation with fractions?
A: Cross-multiply to eliminate fractions first. Then solve like a regular equation.

Q: How do I know which side to move terms to?
A: Move terms to wherever it's easier to simplify. There's no fixed rule, but aim for fewer negative numbers.

Q: Why is my answer wrong even if my steps seem right?
A: Double-check negative signs and arithmetic operations. Small slips can lead to wrong answers.

Q: How can I avoid panicking in exams?
A: Practice similar questions and focus on understanding each step. With practice, the process becomes more automatic.

Q: Are there shortcuts for solving linear equations?
A: Yes, once you understand the basics. Here's the shortcut method I teach my students: simplify and combine like terms first.

Practise with free question sets

Work through more exam-style questions with answers and step-by-step solutions:

• 30+ Secondary 2 Linear equations Practice Questions for 2026 (based on Singapore MOE Syllabus)
• Topic study hub

Want unlimited similar questions with AI marking? Practise on Tutorly.sg/app

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