Question

How do you solve and write the following in interval notation: `1/4x+3>=4-1/3x`?

Answer 1

`[12/7,+oo)`

Explanation:

Multiply ALL terms on both sides of the inequality by 12, the LCM of 4 and 3

`(cancel(12)^3xxx/cancel(4)^1)+(12xx3)>=(12xx4)-(cancel(12)^4xx x/cancel(3)^1)`

`rArr3x+36>=48-4x`

collect terms in x on the left side and numeric values on the right side.

add 4x to both sides.

`3x+4x+36>=48cancel(-4x)cancel(+4x)`

`rArr7x+36>=48`

subtract 36 from both sides.

`7xcancel(+36)cancel(-36)>=48-36`

`rArr7x>=12`

`(cancel(7) x)/cancel(7)>=12/7`

`rArrx>=12/7" is the solution"`

`"expressed in interval notation "[12/7,+oo)`