Solve the inequality. Graph the solution set and write it in interval notation.

Question

-2(x-6)-3x<-(3x+4)+2x

Answer 1

-2(x-6)-3x<-(3x+4)+2x

First, let's simplify both sides of the inequality:

-2x + 12 - 3x < -3x - 4 + 2x

Combine like terms:

-5x + 12 < -x - 4

Next, let's get rid of the fractions by multiplying both sides of the inequality by -1 (and flipping the inequality sign):

5x - 12 > x + 4

Combine like terms:

4x > 16

Divide both sides of the inequality by 4:

x > 4

The solution set, in interval notation, is (4, infinity).
The graph of the solution set would be an open circle on 4, with the line extending to the right indefinitely.