Question

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

Answer 1

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]}