How do you solve \frac { x - 1} { 2} \geq \frac { x } { 3} + 2?

1 Answer
Feb 1, 2017

x >= 15

Explanation:

To get rid of the denominators, you could multiply by 2 or 3, but this would only take care of one problem. Because of this, its typically best to multiply both sides by (2 and 3's) least common factor, which is 6:

(6(x-1))/2 >= (6x)/3 + 12

Since 6 > 0, the inequality remains the same. If we multiplied (or divided) by a negative number, it would be reversed. Then, we can do some simplifications on the fractions, because

6/2 = 3 and 6/3 = 2.

3(x-1) >= 2x + 12

3x - 3 >= 2x + 12

3x - 2x cancel(-3) cancel(+3) >= cancel(2x) cancel(-2x) + 12 + 3

x >= 15