Question

Which of the following is the correct graph of the solution to the inequality −8 ≥ −5x + 2 > −38?

number line with an open dot at 2 with shading to the left and another open dot at 8 with shading to the right
number line with an open dot at 8 and at 2 with shading in between
number line with a closed dot on 2 and an open dot on 8 and shading in between
number line with closed dots at 2 and 8 with shading between the 2 and the 8

Answer 1

We want to see which would be the correct graph of a given inequality.

We will see that the correct option is the third one:

"number line with a closed dot on 2 and an open dot on 8 and shading in between"

Here the inequality is:

-8 ≥ −5x + 2 > −38

Let's simplify this, first we can subtract 2 in the 3 parts of the inequality:

-8 - 2 ≥ −5x + 2 - 2 > −38 - 2

-10 ≥ −5x  > −40

Now we can divide the 3 parts by -5, notice that as it has a negative sign, the direction of the symbols must change:

-10/-5 ≤ −5x/-5 < −40/-5

2 ≤ x < 8

Then the graph will be a solid dot at x = 2 (because x = 2 is a valid solution) that extends to the right unitl it hits an open dot at x = 8 (because x = 8 is not a solution).

Thus the correct option is the third one:

"number line with a closed dot on 2 and an open dot on 8 and shading in between"

If you want to learn more, you can read:

https://brainly.com/question/15748955