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

Oct 2, 2017

See below.

#### Explanation:

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

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

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

Subtract $12$ from both sides:

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

Collect terms:

$0.1 x > - 6$

Divide by 0.1

$x > - 60$

$\left\{x \in \mathbb{R} | - 60 < x < \infty\right\}$

To graph:

From $x > - 60 \implies x + 60 > 0$

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]}