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

Jun 20, 2018

$\left(- 5 , + \infty\right)$

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 $+ \infty$ belongs to the solution set.

Thus, in interval notation, it can be written as $\left(- 5 , + \infty\right)$.