Grade 9 Equations: Short Notes

9 ශ්‍රේණිය · 14 පරිච්ඡේදය · සමීකරණ

85%

of Grade 9 term tests include it (34 of 40)

315

marks in past papers (54 questions)

10 min

full lesson with quick checks

🎯 What you'll learn

Solve linear equations with two types of brackets
Solve linear equations with fractional terms by using the LCM
Form a linear equation from a word problem and solve it
Solve simultaneous equations when one unknown has equal coefficients
Check every answer by substitution

Avurudu sweets

At an Avurudu stall in Ratnapura, 2 kavum and 3 kokis cost Rs. 190, while 2 kavum and 1 kokis cost Rs. 110. Nobody tells you the price of one kokis. With two equations and one clever step, you can work it out in under a minute.

Keep the balance

An equation is like a balanced scale: both sides are equal.To solve it, do the same thing to both sides using inverse operations:• + undoes −, and − undoes +• × undoes ÷, and ÷ undoes ×Undo the outside layers first, one step at a time.Finish by substituting your answer back to check it.

✏️ Two types of brackets

Solve 2[3(x − 1) + 4] = 26.

1Divide both sides by 2: 3(x − 1) + 4 = 13.
2Subtract 4 from both sides: 3(x − 1) = 9.
3Divide by 3: x − 1 = 3, so x = 4.
4Check: 2[3(3) + 4] = 2 × 13 = 26 ✓

✅ x = 4

⚠️ Using the wrong inverse

O/L examiners report this every few years: students use the wrong inverse operation, or undo things in the wrong order.For x/4 + 3 = 8: first subtract 3 (x/4 = 5), then multiply by 4 (x = 20). Writing x = 8 × 4 − 3 = 29 undoes them in the wrong order.Always check: 20/4 + 3 = 8 ✓

Fractions? Clear them first

When an equation has fractions, find the LCM of the denominators.Multiply every term on both sides by it. The denominators cancel and you get an equation with whole numbers.Put each numerator in brackets before multiplying: (x + 2)/3 × 12 becomes 4(x + 2).

✏️ Two fractions

Solve x/3 + x/4 = 7.

1LCM of 3 and 4 is 12. Multiply every term by 12.
24x + 3x = 84, so 7x = 84.
3x = 12. Check: 4 + 3 = 7 ✓

✅ x = 12

⚠️ The minus belongs to the whole bracket

Two slips with fractions:1. −3(x − 1) written as −3x − 3. The minus multiplies both terms: −3x + 3.2. Multiplying only the fractions by the LCM and forgetting the right-hand side. In the example above, 2 must become 2 × 12 = 24, not stay 2.

Simultaneous equations

Two unknowns need two equations that are true at the same time.If one unknown has the same coefficient in both:• same sign → subtract the equations• opposite signs → add themThat unknown disappears. Solve for the other, then substitute back.Or use substitution: make one unknown the subject and put it into the other equation.

📌 Remember

• Do the same to both sides, using inverse operations in the right order.• Brackets: undo the outside first, or expand carefully (a minus changes every sign inside).• Fractions: multiply every term, both sides, by the LCM.• Simultaneous equations: same coefficient → same signs subtract, opposite signs add.• Always substitute your answer back to check.

🧾 Quick revision sheet

What is an inverse operation?	The operation that undoes another: + and −, × and ÷.
How do you clear fractions in an equation?	Multiply every term on both sides by the LCM of the denominators.
Expand −2(x − 5)	−2x + 10
Simultaneous equations: same coefficient, same sign	Subtract the equations.
Simultaneous equations: same coefficient, opposite signs	Add the equations.
How do you check a solution?	Substitute it into the original equation(s); both sides must be equal.

Now test yourself: 4 quick checks and 3 more worked examples

The full lesson checks your answers as you go, and Gedara Sir tracks which parts you've got.

📖 Start the 10-minute lesson free ▶ Practise 5 past-paper questions