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2 votes
What is the graph of the solution to the following compound inequality?

3-x22 or 4x+2210
O A.
B.
O c.
O D.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
H
He
+++
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
5 6 7 8 9 10
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
4
€1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
5 6 7 8 9 10
3 4 5 6 7 8 9 10

User Piwaf
by
8.1k points

1 Answer

3 votes

Answer:

Explanation:

To graph the solution to the compound inequality 3 - x < 22 or 4x + 2 > 10, we need to graph the individual inequalities and find the overlapping region.

First, let's graph the inequality 3 - x < 22:

Subtract 3 from both sides to isolate x:

-x < 19

Multiply both sides by -1, which reverses the inequality direction:

x > -19

This means that x is greater than -19, but not including -19. So, we will have an open circle at -19 and shade everything to the right of it.

Next, let's graph the inequality 4x + 2 > 10:

Subtract 2 from both sides to isolate 4x:

4x > 8

Divide both sides by 4:

x > 2

This means that x is greater than 2, but not including 2. So, we will have an open circle at 2 and shade everything to the right of it.

Combining the two inequalities, we need to find the overlapping region. Since both inequalities have an open circle at their endpoint, we will use a dashed line to represent them.

The graph should look like this:

markdown

Copy code

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

+ +

| |

| |

+---------------------------------|-------------------->

-19 2

The shaded region will be to the right of -19 and to the right of 2, including all numbers greater than those values.

Therefore, the correct answer is:

O A. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

User Muhammet Ali Asan
by
7.9k points
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