A letter holds a place for a number, so you can work with the number before you know it.
The words you need
| Word | What it means | In 5x² − 3x + 7 |
|---|---|---|
| Term | A part separated by a plus or minus sign | Three terms |
| Coefficient | The number in front of the letter | 5 and −3 |
| Variable | The letter itself | x |
| Constant | A term with no letter in it | 7 |
Like terms have exactly the same letters raised to exactly the same powers. 3x and 3x² are not like terms.
Only like terms can be added
3x plus 5x is 8x, just as 3 apples plus 5 apples is 8 apples. But 3x plus 5y stays as it is.
If x is 2 and y is 4, then 3x + 5y is 26 while 8xy would be 64. Substituting numbers settles any doubt.
Substitution
Replace each letter by its number, doing the multiplications before the additions.
2x means 2 multiplied by x, so when x is 3 the value is 6 and not 23. The multiplication sign is always there, just not written.
Five less than a number is x minus 5, not 5 minus x. Naming the letter first prevents most of the errors.
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