A letter stands for a number
In algebra a letter stands for a number. Often it is a number we do not know yet, and the letter holds its place until we find it. The letter used most often is x, but any letter will do.
Picture a balance scale. On the left pan is x, and on the right pan is 5. The scales are perfectly level, so the two pans weigh the same. Whatever number x stands for, it weighs the same as 5, so x = 5.
The pans are level, so x weighs the same as 5: x = 5.
A letter inside an expression
Now the left pan holds x and 2 more, written x + 2, and the right pan holds 7. The scales are still level, so x + 2 = 7. Two amounts joined by an equals sign make an equation.
The letter x still stands for one particular number. Ask which number makes 7 when 2 is added to it. 5 + 2 = 7, so x = 5.
x and 2 together weigh the same as 7, so x on its own is 7 − 2 = 5.
Only one number fits
Try other numbers in place of x and the scales stop being level. If x were 4, the left pan would hold 4 + 2 = 6, which is less than 7, so the scales would tip down on the side of the 7. If x were 6, the left pan would hold 6 + 2 = 8, which is more than 7, and they would tip the other way. Only 5 keeps them level.
With 4 in place of x, the left pan holds 6, less than 7, so the scales tip toward the 7.
How letters are written
A number written just in front of a letter means multiply. 3x means 3 × x, three lots of x, and when x = 5, 3x is 3 × 5 = 15. The multiplication sign is left out because × looks too much like the letter x.
Wherever the same letter appears in one problem, it stands for the same number. In x + x = 10, both letters are 5, because 5 + 5 = 10.
The same number, 5, goes into both places where x stands, and 5 + 5 = 10.
The usual mistakes
In x + 2 = 7, x is not 7. The 7 is the whole right pan, which weighs the same as x and the 2 together, not x alone.
x is not 2 either. The 2 is the number added to x. x is what is left of 7 once the 2 is taken away, which is 5.