If 1 is subtracted from a number and the difference is tripled, the result is 9 more than the number. Find the number.

Answer 1

"a number" will be represented by x.

"If 1 is subtracted from a number" is x-1.

"and the difference is tripled" would be 3 * (x - 1).

This is part one of the equation.

The second part, "the result is 9 more than the number" would be x + 9.

The question states that these two portions are to be equal, so part 1 = part 2:

3 * (x - 1) = x + 9 - multiply the 3 across both x and -1 in the parentheses

3x - 3 = x + 9 - simplify for x

2x - 3 = 9

2x = 9 + 3

2x = 12

2x/2 = 12/2

x = 6

To prove the initial question we can show that:

"If 1 is subtracted from a number" : 6 - 1 = 5

"and the difference is tripled" 5 * 3 = 15

"the result is 9 more than the number" 15 - 6 = 9