How do you solve and write the following in interval notation: # -12(x-4) +3 > 4x - 4 - 5x#?

1 Answer
Jun 20, 2018

Answer:

#(-5,+oo)#

Explanation:

In interval notation:
'[' denotes greater than or equal to;
']' denotes less than or equal to;
'(' denotes greater than;
and ')' denotes less than.

To solve this equation, evaluate all terms and isolate #x# on one side.

#−12(x−4)+3>4x−4−5x# => Given

# (−12x+48) +3>4x−4−5x# => Distributing -12

# −11x>−55# => Isolating #x# to the left side

# x<5# => Dividing by -11 (reversing the sign)

This implies that any number between 5 and #+oo# belongs to the solution set.

Thus, in interval notation, it can be written as #(-5,+oo)#.