Question

Solve the inequality x + 2 1/2 > -1/2. Graph the solution set on a number line.show your work.

Answer 1

x > - 3

Explanation:

x + 2
`(1)/(2)` > -
`(1)/(2)` First turn 2
`(1)/(2)` into an fraction since its easier. So it becomes
`(5)/(2)`

x +
`(5)/(2)` > -
`(1)/(2)`

-
`(5)/(2)` -
`(5)/(2)` Do inverse operations, so subtract
`(5)/(2)` from both sides.

x > -
`(6)/(2)` Combine -
`(5)/(2)` with -
`(1)/(2)`, which gives us -
`(6)/(2)`

x > - 3 Since we know that 6 divided by 2 is 3.

This would not allow me to attach an image so I am going to type a visual representation f what the graph would look like below)

<-------------O--------------------------------------------------->

-5 -4 -3 -2 -1 0 1 2 3 4 5

So, the number line would be a solid line rather than dashed (but I was not able to attach an image so I kind of had to improvise). When using ≥ ≤ sings the circle of the point is closed. When using < and > signs, the circle of the point is open. Thus, in this scenario since he sign is >, then the circle of the point is open. The direction of the arrow and ray for this equality is going to the right because the answer is that x is greater than - 3, Therefore any values greater than - 3 are a possibility which is why the arrow goes on indefinitely.