19 increased by four times a number is 51

Answer 1

to "translate" this sentence into math, you need to understand what the words are saying.

"19 increased" means that you are making the number 19 bigger - addition. The word "by" tells you that what follows is the quantity that is increasing or added to 19. "four times" means you are multiplying what follows by 4, "a number" means that it is something you don't know, so a variable will be assigned, say "n". Since the whole of "four times a number" is added to 19, I recommend you enclose it in parentheses to indicate that it as a whole is added to 19.. the word "is" nearly always means "equals" or " = ". 51 is the object of the equal sign.

Putting it all together:

19 + (4*n) = 51 OR 19 + 4*n = 51

In this case, the part that is added to 19 does not have to be in parentheses because the order of operations says that the multiplication is done first, but it is a good idea to get in the habit of using parentheses when this happens because they would be required if it has been "4 and a number" (4 + n) or "4 less a number" (4 - n)

Answer 2

The problem is equivalent to

19+4X = 51

Subtract 19 from both sides

4X = 32

Divide both sides by 4 to get

X=8