We will start by writing a compound inequality to represent the situation. Then we will graph it. Let x represent the child's weight expressed in pounds. We know that a child must weight at least 15 pounds — in other words, the child's weight must be greater than or equal to 15 pounds.
x≥ 15
At the same time the child's weight must be no more than 35 pounds, so it is less than or equal to 35 pounds.
x≥ 15 and x≤ 35We have obtained a compound inequality, and its graph will model the situation. Now let's graph it! To do so we will start by graphing each of the single inequalities.
First Inequality
The first inequality is x≥ 15. This inequality tells us that all values greater than or equal to 15 will satisfy the inequality.
Note that the point on 15 is closed, because it satisfies the inequality.
Second Inequality
The second inequality is x≤ 35. This inequality tells us that all values less than or equal to 35 will satisfy the inequality.
Note that the point on 35 is closed, because it satisfies the inequality.
Compound Inequality
The graph of an and compound inequality is the intersection of the graphs of the single inequalities.
