Question

If 6 times a certain number is added to8, the result is 32. Which of the following equations could be used to solve the problem

Answer 1

This used to confuse me, too. We can use a variable to represent a number we don't know.

In elementary school, you had a problem that said 3 + _ = 8 and you could figure out the blank was 5.

Instead, we have 3 + x = 8 and we can figure out that x = 5.

We can also be given a value for x and asked something like if x = 8, what is x + 7, which we know is 15.

In algebra, when we multiply by a variable, we just say how many of that variable it is. Twelve times a variable is 12x or 12a or 12q, depending on what letter we decide to use to represent our variable.

So, six times a certain number, which we are spparently calling x, is 6x. Adding 8 to that is 6x + 8. Those do not combine to make 14 or 14x because one term has the variable and one does not.

If the result is 32...

6x + 8 = 32

Let's look at the other options.

6x = 32. Where's the 8 added??

6(x + 8) = 32. Well, that looks like it could be it, buuuuut we'd multiply 6 by everything in the parentheses, so this is 6 times the sum of a number and 8 is 32, or 6x + 48 = 32. Not quite.

6x = 8 + 32. That's six times a number equals the sum of 8 and 32, right? Thaaaat's not what it says.