In addition to solving simple equations, at the higher level you also need to know how to solve equations with fractions.
Fractions
How do we solve the equation x/2 − 4 = 3?
One way is to multiply everything by 2:
x/2 − 4 = 3
x - 8 = 6
x = 14
Or, alternatively, add 4 and then multiply both sides by 2:
x/2 − 4 = 3
x/2 = 7
x = 14
- Question
Solve the equation: 4 − x/3 = 1
- Answer
Method 1
4 − x/3 = 1
(multiply by 3) 12 − x = 3
(add x) 12 = 3 + x
(minus 3) x = 9
Method 2
4 − x/3 = 1
(add x/3) 4 = 1 + x/3
(minus 1) 3 = x/3
(multiply 3) x = 9
- Question
A number is doubled and divided by 5. This has the same answer as 3 more than the number divided by eight. What is the number?
- Answer
First write out the information as an equation.
- Call the number x.
- A number is doubled and divided by 5 can be written 2x/5
- And 3 more than the number divided by eight can be written (x + 3)/8.
- So we have
- 2x/5 = (x + 3)/8
- 40 ( 2x/5) = 40 ( (x + 3)/8) (Multiply both sides by 40)
- 8 ( 2x ) = 5 (x + 3) (cancelling out)
- 16x = 5x + 15 (multiplying out the brackets)
- 11x = 15
- So
- x = 15/11 = 1 4/11
Now try a Test Bite
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