How do you solve, graph and write set-builder notation for the answer #0.6x + 12 + x >2x + 6 - 0.5x#?

1 Answer
Oct 2, 2017

Answer:

See below.

Explanation:

By addition and subtraction move all terms of #x# to one side of the inequality:

#0.6x+12+x> 2x+6-0.5x#

#0.6x +12 +x +0.5x -2x>6#

Subtract #12# from both sides:

#0.6x +x +0.5x -2x>6-12#

Collect terms:

#0.1x> -6#

Divide by 0.1

#x> -60#

#{x in RR | -60< x < oo }#

To graph:

From #x> -60 => x+60>0#

We can the plot the line #x = -60#

This will give us a boundary line between the included and excluded regions. This will have a dashed line because it is a less than and not a less than or equal to. The shaded region will be to the right of this .i.e. where #x# is greater than #-60#

graph:

graph{x > -60 [-80, 10, -5, 5]}