what is three times a number increased by nine is five

Question

please help me figure this out so I can explain to my son

Answer 1

So we have a unknown number; let's call it x.

The trick here is how you read it. At first you might think you're multiplying before adding, but the way it is written--increased by--infers that the addition is done first. That gives us the following equation:

3(x + 9) = 5

Divide both sides by 3:

3(x + 9) / 3 = 5 / 3

x + 9 = ⁵/₃

And now we subtract 9 from both sides:

x + 9 - 9 = ⁵/₃ - 9

x = ⁵/₃ - 9

Let's convert that 9 into an improper fraction so that we can subtract it a whole lot easier. Multiply it by ³/₃ (because ³/₃ equals 1):

x = ⁵/₃ - 9 * ³/₃

x = ⁵/₃ - ²¹/₃

Now we can subtract the numerators:

x = -¹⁶/₃ in improper form, or -5 ¹/₃ as a mixed number