Question

Which is the solution to the inequality?

23/5 < b-8/15

Answer 1

b > 77/15

Explanation:

`(23)/(5) < b - (8)/(15) \\ - b < - (8)/(15) - (23)/(5) \\ - b \: < - ( 8)/(15) - (69)/(15) \\ - b < - (77)/(15) \\ - b < - 5 (2)/(15) \\ b > 5 (2)/(15)`

Or

23/5 < b - 8/15

69/15 < b - 8/15

77/15 < b

B > 77/15

Answer 2

`b > (77)/(15)`

Explanation:

We have the inequality

`(23)/(5) < b-(8)/(15)`

Switch sides:

`b-(8)/(15) > (23)/(5)\\\\\\\mathrm{Add\:}(8)/(15)\mathrm{\:to\:both\:sides}:\\\\b-(8)/(15)+(8)/(15) > (23)/(5)+(8)/(15)\\\\`

Left side is b

Right side is evaluated as follows

`(23)/(5) = (69)/(15) \quad\quad\text{(multiply numerator and denominator by 3)}`

`(23)/(5)+(8)/(15) = (69)/(15)+(8)/(15) \\\\= (77)/(15)`

So the inequality becomes

`b > (77)/(15)`