Grade 5 Mathematics : Algebra – Simple Equations Notes

Mathematics — Algebra

Subtopic: Simple Equations (for age 10)

An equation is like a balanced scale. It tells us that two things are equal. In algebra we use a letter (often x) for a number we do not know yet. Our job is to find that number so the two sides are equal.

Idea: Think of "x + 5 = 12" as a scale. If you take 5 from the side with x + 5, you must also take 5 from the other side (12) to keep it balanced.

One-step equations (Addition or Subtraction)

If x + a = b, subtract a from both sides: x = b − a. If x − a = b, add a to both sides: x = b + a.

Example 1
Equation: x + 5 = 12
Step 1: Subtract 5 from both sides → x + 5 − 5 = 12 − 5
Step 2: So x = 7
Check: Put x = 7 into the equation: 7 + 5 = 12 ✔

Example 2
Equation: x − 3 = 9
Step 1: Add 3 to both sides → x − 3 + 3 = 9 + 3
Step 2: So x = 12
Check: 12 − 3 = 9 ✔

One-step equations (Multiplication or Division)

If a·x = b, divide both sides by a: x = b ÷ a. If x ÷ a = b, multiply both sides by a: x = b × a.

Example 3
Equation: 3x = 15
Step 1: Divide both sides by 3 → x = 15 ÷ 3
Step 2: x = 5
Check: 3 × 5 = 15 ✔

Example 4
Equation: x ÷ 4 = 6
Step 1: Multiply both sides by 4 → x = 6 × 4
Step 2: x = 24
Check: 24 ÷ 4 = 6 ✔

Two-step equations

Do the inverse (opposite) of the last operation first. Example: if 3x + 4 = 16, subtract 4, then divide by 3.

Example 5
Equation: 3x + 4 = 16
Step 1: Subtract 4 from both sides → 3x = 12
Step 2: Divide both sides by 3 → x = 4
Check: 3×4 + 4 = 12 + 4 = 16 ✔

Unknowns on both sides

Bring unknowns to one side by adding or subtracting. Then solve as before.

Example 6
Equation: 2x + 5 = x + 9
Step 1: Subtract x from both sides → 2x − x + 5 = 9 → x + 5 = 9
Step 2: Subtract 5 from both sides → x = 4
Check: 2×4 + 5 = 8 + 5 = 13 and x + 9 = 4 + 9 = 13 ✔

Visual: Balance model

x + 5

Remove 5 from both sides (take away 5 from each side) to keep the balance: x = 7.

Tips to remember

Do the same thing to both sides of the equation.
Undo the operations in reverse order (last step first).
Always check your answer by putting it back into the equation.

Practice problems (try these)

x + 6 = 14
x − 7 = 3
4x = 20
x ÷ 5 = 2
2x + 3 = 11
5 + x = 12
3x − 4 = 11
2x + 5 = x + 9

Answers

x = 8
x = 10
x = 5
x = 10
x = 4
x = 7
x = 5
x = 4

Good work! Practise more equations. If you get stuck, draw the balance (left and right) and remove the same amount from both sides.

Prepared for Kenyan learners (age ~10). Use these notes to practise and ask your teacher for more examples.

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Grade 5 Mathematics Algebra – Simple Equations Notes