6. Compound Inequalities
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An "and" inequality is written with the variable between two inequality symbols.
Compound inequality: 0≤ x <8
Reading the given phrases, we can identify two inequalities.
Let's look at these pieces one at a time.
x≥ 0 To graph this inequality, we place a closed circle at 0 (since 0 is included) on a number line and then shade everything to the right of this point.
The phrase "less than 8" describes all numbers to the left of, but not including, 8. We can write this as an inequality as well. x<8 We can graph this by placing an open circle at 8 on a number line and then shading everything to the left of this point.
Since both inequalities should apply, we can combine them into the following compound inequality. 0≤ x <8 Graphically, the solution set is the overlap between the red and the blue graph, shown as the purple graph below.
