Question

How do you solve `\frac { x } { 3} + 2> \frac { 2x } { 5} + \frac { 17} { 15}`?

Answer 1

`x<13`

Explanation:

We can combine fractions by finding a common denominator, which in this case is 15. We can give all the fractions a denominator by using creative versions of the number 1 (and also seeing that `2=2/1`)

`x/3+2 > (2x)/5+17/15`

`x/3(1)+2/1(1) > (2x)/5(1)+17/15(1)`

`x/3(5/5)+2/1(15/15) > (2x)/5(3/3)+17/15(1/1)`

`(5x)/15+30/15 > (6x)/15+17/15`

We can now multiply by 15 throughout the entire inequality (which in the end means we can work solely with the numerators)

`5x+30 > 6x+17`

`5xcolor(red)(-5x-17)+30 > 6xcolor(red)(-5x-17)+17`

`13 > x`