Simple Equations Notes, Quizzes & Revision
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Mathematics โ 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.
One-step equations (Addition or Subtraction)
If x + a = b, subtract a from both sides: x = b โ a. If x โ a = b, add a to both sides: x = b + a.
Equation: x + 5 = 12
Step 1: Subtract 5 from both sides โ x + 5 โ 5 = 12 โ 5
Step 2: So x = 7
Check: Put x = 7 into the equation: 7 + 5 = 12 โ
Equation: x โ 3 = 9
Step 1: Add 3 to both sides โ x โ 3 + 3 = 9 + 3
Step 2: So x = 12
Check: 12 โ 3 = 9 โ
One-step equations (Multiplication or Division)
If aยทx = b, divide both sides by a: x = b รท a. If x รท a = b, multiply both sides by a: x = b ร a.
Equation: 3x = 15
Step 1: Divide both sides by 3 โ x = 15 รท 3
Step 2: x = 5
Check: 3 ร 5 = 15 โ
Equation: x รท 4 = 6
Step 1: Multiply both sides by 4 โ x = 6 ร 4
Step 2: x = 24
Check: 24 รท 4 = 6 โ
Two-step equations
Do the inverse (opposite) of the last operation first. Example: if 3x + 4 = 16, subtract 4, then divide by 3.
Equation: 3x + 4 = 16
Step 1: Subtract 4 from both sides โ 3x = 12
Step 2: Divide both sides by 3 โ x = 4
Check: 3ร4 + 4 = 12 + 4 = 16 โ
Unknowns on both sides
Bring unknowns to one side by adding or subtracting. Then solve as before.
Equation: 2x + 5 = x + 9
Step 1: Subtract x from both sides โ 2x โ x + 5 = 9 โ x + 5 = 9
Step 2: Subtract 5 from both sides โ x = 4
Check: 2ร4 + 5 = 8 + 5 = 13 and x + 9 = 4 + 9 = 13 โ
Visual: Balance model
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 โ 7 = 3
- 4x = 20
- x รท 5 = 2
- 2x + 3 = 11
- 5 + x = 12
- 3x โ 4 = 11
- 2x + 5 = x + 9
- 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.