Question

How do you solve for b? b+7>`3/2b`+17

Answer 1

`b<-20`

Explanation:

`b+7>3/2b+17`

For ease, let's multiply through by 2 to get rid of the fraction:

`2b+14>3b+34`

Let's now group like terms:

`2bcolor(red)(-2b-34)+14>3bcolor(red)(-2b-34)+34`

`-20>b`

To show this graphically, draw an open circle around `-20` on a number line (to show that it isn't part of the solution), and then draw a ray heading off towards `- oo`.

Answer 2

`b<-20`

Explanation:

`b+7>3/2`b`+17`

add `-17` both sides;
`b+7-17>3/2b` `+17-17`
`b-10>3/2b` (add -b both sides)
`-b+b-10>3/2b-b`
`-10>1/2b`(multiply by 2 both sides)
`2*(-10)>2*(1/2b)`
`-20>b`
in other words;

`b<-20`