An "and" inequality is written with the variable between two inequality symbols.
Compound inequality: 28.5≤ x≤ 29 Graph:
Practice makes perfect
We are looking for numbers that are greater than or equal to 28.5 and at the same time they have to be less than or equal to 29. We can identify two inequalities.
First inequality: Greater than or equal to 28.5.
Second inequality: Less than or equal to 29.
Let's look at these pieces one at a time.
First inequality
According to the statement, we are looking for all real numbers greater than or equal to 28.5. We can write this as the following inequality.
x≥ 28.5
To graph this inequality, we place a closed circle at 28.5 (since 28.5 is included) on a number line and then shade everything to the right of this point.
Second inequality
The phrase "less than or equal to 29" describes all numbers to the left of 29, inclusive. We can write this as an inequality as well.
x≤ 29
We can graph this by placing a closed circle at 29 on a number line and then shading everything to the left of this point.
Compound inequality
Since both inequalities should apply, we can combine them into the following compound inequality.
28.5≤ x≤ 29
Graphically, the solution set is the overlap between the red and the blue graph, shown as the purple graph below.
