First algebra and simple equations · Usually met around P5
Simple equations
Undo the steps in reverse order.
How to do it
Method
Undo the steps in reverse order
Undo it: 20 − 5 = 15, 15 ÷ 3 = 5
Another way
The same to both sides
Both sides − 5: 20 − 5 = 15; both ÷ 3: 15 ÷ 3 = 5
In full
Solving an equation means finding the number that x stands for. The quick way is to undo each step in reverse. In 3x + 5 = 20, x was multiplied by 3 and then 5 was added to make 20. So undo it backwards: take away 5, then divide by 3. 20 − 5 = 15, 15 ÷ 3 = 5, so x = 5. To undo x ÷ 4 = 9, multiply: 9 × 4 = 36. Or do the same thing to both sides of the equation. Take 5 from both sides: 3x = 15. Divide both sides by 3: x = 5. Check by putting it back: 3 × 5 + 5 = 20.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
x ÷ 2 = 3, x = ?
Show the answer and working
Answer: x ÷ 2 = 3, x = 6
x ÷ 2 = 3: undo it in reverse, 3 × 2 = 6, so x = 6
Example 2
6x = 72, x = ?
Show the answer and working
Answer: 6x = 72, x = 12
6x = 72: undo it in reverse, 72 ÷ 6 = 12, so x = 12
Example 3
x − 14 = 11, x = ?
Show the answer and working
Answer: x − 14 = 11, x = 25
x − 14 = 11: undo it in reverse, 11 + 14 = 25, so x = 25
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