Most students meeting algebra for the first time wonder why anyone would want to add a letter to a number. But that is not what it's all about. The letter x stands for a number. We could just write ? Instead of x. So what would 3?+5 mean? It's as if someone said: think of a number, multiply it by 3 and add 5 to the result. So x is that unknown number. Any letter could have been used. 3x+5 means 3*x+5; x stands for any number you can think of, so we don't have to write a whole load of sums: 3*1+5, 3*7+5, 3*10+5, for example. Just by writing 3x+5 we are actually giving an instruction: multiply a number by 3 and then add 5 to the result. And note that x can be a fraction, or it can be negative. It doesn't matter: the instruction is the same: multiply the number by 3 and add on 5. The beauty of algebra is that if someone told you that they thought of a number, multiplied it by 3, added 5 then told you the result was 29, then using the rules of algebra you could find out what number they thought of. Algebra tells you the answer is 8, because 3*8+5=29. (You write 3x+5=29 to make an equation. Subtract 5 from each side of the equation: 3x+5-5=29-5; 3x=24; now divide both sides by 3: x=24/3=8. Try it with your friends. Ask them to think of a number without telling you, multiply it by 3 then add 5 and give you the result. Now you know why we represent numbers by letters sometimes.)