Problem:
- How many people voted for the Green Party if 2,000 votes are for other parties and there are 3,250 votes in the ballot box?
-
x is the number of votes for the Green Party.
2,000 is the number of votes for other parties.
3,250 is the total number of votes.
-
x + 2,000 = 3,250
x = 3,250 — 2,000x = 1,250 -
There are 1,250 votes for the Green Party.
An equation can be more complex, but you can always solve it in the same way:
- Put all the like terms in the same member.
(Remember: in the term 5x, x is the literal part, because it is a letter; 5 is a numerical coefficient, because it is a number.
Like terms are terms which are alike (= similar) because they have the same literal part, for example 5x and 3x and —6x, or no literal part, like 7, 11 and —20).
- Do the operations in each member; we need to have only one term in each member.
- Find out x (if it has a numeric coefficient, for example 3x).
Here is another example:
Problem:
For my birthday, my mother gave me some money. Then my father gave me double that amount. Then my grandparents gave me
three times as much as my mother. I had £3 in my piggy bank, and now I have £15. How much did my mother give me?
-
x is what my mother gave me.
2x is what my father gave me.
3x is what my grandparents gave me.
£3 is what I had in my piggy bank.
£15 is what I have now.
| x + 2x + 3x + 3 = 15 | |
| 1st step —put all the like terms in the same member: | |
|
x + 2x + 3x = 15 — 3 |
|
| 2nd step —do the operations to get only one term in each member: | |
| 6x = 12 | |
| 3rd step —isolate x: | |
 x = 2 |
JJCC