Question

1) If one-third of a number is 6 less than half of the number, what is the number?

Solve Algebraically

Answer 1

Explanation:

let the number be x

`1 / 3 \: of \: x \\ x / 3 = 1 / 2 \: of \: x - 6 \\ x / 3 = x / 2 - 6 \\ multiply \: both \: sides \: by \: the \: lcm \: 6 \\ x / 3 * 6 = x / 2 * 6 - 6 * 6 \\ x * 2 = x * 3 - 36 \\ 2x = 3x - 36 \\ 2x - 3x = - 36 \\ - x = - 36 \\ divide \: both \: sides \: by \: - 1 \\ - x / - 1 = - 36 / - 1 \\ x = 36`