Inequality with fractions: x/4<(5x-2)/3-(7x-3)/5

[Guest]

Solve the inequality with fractions:
[tex]\frac{x}{4} < \frac{5x-2}{3} - \frac{7x-3}{5}[/tex]

[Guest]

First you have to find the least common multiple of 4,3,5
LCM(4,3,5) = 4 * 3 * 5 = 60
then multiply the both sides of the equeation by 60(multiply every fraction by 60)

[Guest]

Here is the solution of the inequality:

[tex]\frac{x}{4} < \frac{5x-2}{3} - \frac{7x-3}{5}[/tex]

[tex]\frac{x}{4} * 60 < (\frac{5x-2}{3} - \frac{7x-3}{5}) * 60[/tex]

[tex]\frac{x}{4} * 60< \frac{5x-2}{3} * 60 - \frac{7x-3}{5} * 60[/tex]
15x < (5x-2)*20 - (7x - 3) * 12

15x < 100x - 40 - 84x + 36

15x < 16x - 4

15x - 16x < - 4
-x < -4
x > 4

[Guest]

The definition of this can be defined as the smallest of the common multiples. Also, a common multiple of two numbers that is exactly divisible by each number. Hence, we can define the least common multiple(LCM) of two numbers as the smallest number, which is not equal to zero, which is a multiple of both.
for read more about this then go to link:
http://www.mathcaptain.com/number-sense/least-common-multiple.html