Question

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

Answer 1

Answer:

x > - 3

Step-by-step explanation:

x + 2$\frac{1}{2}$ > - $\frac{1}{2}$      First turn 2$\frac{1}{2}$ into an fraction since its easier. So it becomes $\frac{5}{2}$

x + $\frac{5}{2}$ > - $\frac{1}{2}$

  - $\frac{5}{2}$     - $\frac{5}{2}$         Do inverse operations, so subtract $\frac{5}{2}$ from both sides.

    x > - $\frac{6}{2}$          Combine  - $\frac{5}{2}$ with - $\frac{1}{2}$, which gives us - $\frac{6}{2}$

    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.