Question

Which compound inequality is represented by the graph?

1) –11.25 < x ≤ –8.75

2) x –11.25 or x > –8.75

3) –8.75 x < –11.25

4) x < –8.75 or x –11.25

Answer is 2

Answer 1

B; x –11.25 or x > –8.75

Answer 2

Answer: Option 2.

Explanation:

When you graph inequalities on a number line:

The closed circle represent the inequalities "
`\leq` and "
`\geq`", because that point belongs to the solution.

The opened circle is used to represent the inequalities "<" and ">", because that point does not belong to the solution.

Compound inequalities are separated by the words:

- "and" (Which indicates the intersection of the sets).

- "or" (Which indicates the union of the sets.)

You can observe in the graph that:

There is a closed circle at the point 11.25 (which indicates that it is part of the solution) and the line continues to the numbers less than 11.25. This means that:

`x\leq-11.25`

There is an opened circle at the point -8.75 (which indicates that it is not part of the solution) and the line continues to the numbers greater than -8.75. This means that:

`x\geq-8.75`

Therefore, the solution is all the values of "x" in which this is:

`x\leq -11.25\ or\ x>-8.75`