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what does it mean if a letter is next to a number in algebra e.g. 5a = 65

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The number 5 is the coefficient on the variable a. All this means is that 5 "times" a equals 65. 
If the directions were to solve, were trying to find the number that when multiplied by 5 will give us 65. The way we do this algebraically is to undo the multiplication of a by 5, by dividing both sides of the equation by 5.
This gives us a = 13.
To check, we can see that 5*13=65.