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Compound Inequalities

Write compound inequalities from graphs

What compound inequality describes this graph?

Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3 .

Solution:

Remember:

• When a compound inequality has a graph that looks like a line segment, it can be written with the variable between the values of the endpoints, like 1 < x < 3 .

• When a compound inequality has a graph that looks like two rays, it can be written as two inequalities joined with or, like x < 1 or x > 3 .

The graph shows two rays, so the compound inequality can be written as two inequalities joined with or. The ray on the left represents x < 7 . The ray on the right represents x = 8

Use or to connect them: x < 7 or x = 8

What compound inequality describes this graph?

-7 ≤ x < -4
x ≤ -7 or x ≥ -4
-7 ≤ x ≤ -4
x ≤ -7 or x > -4