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

1 Answer
Feb 15, 2017

Answer:

#[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)#