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Then, identify what we are looking for and assign a variable to represent it.Next, restate the problem in one sentence to make it easy to translate into a compound inequality. Example \(\Page Index\) Due to the drought in California, many communities have tiered water rates.For the compound inequality \(x−3\) and \(x\leq 2\), we graph each inequality. The numbers that are shaded on both graphs, will be shaded on the graph of the solution of the compound inequality.
Andrew is creating a rectangular dog run in his back yard. The perimeter of the dog run must be at least 42 feet and no more than 72 feet.
Use a compound inequality to find the range of values for the width of the dog run.
How many hcf can the owner use if he wants his usage to stay in the normal range?
Example \(\Page Index\) Due to the drought in California, many communities now have tiered water rates.
Write a compound inequality that shows the range of numbers that Penelope might be thinking of.
Gregory is thinking of a number and he wants his sister Lauren to guess the number.We will use the same problem solving strategy that we used to solve linear equation and inequality applications.Recall the problem solving strategies are to first read the problem and make sure all the words are understood.We solve each inequality separately and then consider the two solutions.To solve a compound inequality with the word “and,” we look for all numbers that make inequalities known as the intersection of the two inequalities.Penelope is thinking of a number and wants June to guess it.Five more than three times her number is between 2 and 32.His first clue is that six less than twice his number is between four and forty-two.Write a compound inequality that shows the range of numbers that Gregory might be thinking of.To write the solution in interval notation, we will often use the union symbol, ∪∪ to show the union of the solutions shown in the graphs.Situations in the real world also involve compound inequalities.