Stage 9 · Mixed operations
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 finds the number x stands for. The quick way is to undo it in reverse: in 3x + 5 = 20, x was times 3 and then plus 5 to make 20, so undo it backwards: take 5, then divide by 3: 20 − 5 = 15, 15 ÷ 3 = 5, so x = 5. x ÷ 4 = 9 undoes by multiplying: 9 × 4 = 36. Or do the same thing to both sides of the equation: take 5 from both sides, 3x = 15; divide both by 3, x = 5 — the same answer. 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 − 3 = 21, x = ?
Show the answer and working
Answer: x − 3 = 21, x = 24
x − 3 = 21: undo it in reverse, 21 + 3 = 24, so x = 24
Example 2
4x − 2 = 70, x = ?
Show the answer and working
Answer: 4x − 2 = 70, x = 18
4x − 2 = 70: undo it in reverse, 70 + 2 = 72, 72 ÷ 4 = 18, so x = 18
Example 3
6x + 17 = 65, x = ?
Show the answer and working
Answer: 6x + 17 = 65, x = 8
6x + 17 = 65: undo it in reverse, 65 − 17 = 48, 48 ÷ 6 = 8, so x = 8
Example 4
5x − 14 = 86, x = ?
Show the answer and working
Answer: 5x − 14 = 86, x = 20
5x − 14 = 86: undo it in reverse, 86 + 14 = 100, 100 ÷ 5 = 20, so x = 20
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