Gregory is thinking of a number and he wants his sister Lauren to guess the number. The perimeter of the garden must be at least 36 feet and no more than 48 feet. Now that we know how to solve linear inequalities, the next step is to look at compound inequalities. Explain the steps for solving the compound inequality or. There are different rates for Conservation Usage, Normal Usage and Excessive Usage. This graph shows the solution to the compound inequality. The solution covers all real numbers. Solve Compound Inequalities with "and". 54 per hcf for Normal Usage.
The number of hcf he can use and stay in the "normal usage" billing range. When written as a double inequality, it is easy to see that the solutions are the numbers caught between one and five, including one, but not five. Ⓑ What does this checklist tell you about your mastery of this section? We then look for where the graphs "overlap". Let's start with the compound inequalities with "and. " The homeowner can use 16–40 hcf and still fall within the "normal usage" billing range. For example, and can be written simply as and then we call it a double inequality.
Make either inequality. Graph the solution and write the solution in interval notation: Solve Compound Inequalities with "or". Research and then write the compound inequality that shows you what a normal diastolic blood pressure should be for someone your age. By the end of this section, you will be able to: - Solve compound inequalities with "and". Ⓑ Let y be your diastolic blood pressure. Due to the drought in California, many communities now have tiered water rates. Practice Makes Perfect. The systolic blood pressure measures the pressure of the blood on the arteries as the heart beats. The bill for Conservation Usage would be between or equal to? The number two is shaded on both the first and second graphs. To solve a compound inequality with the word "or, " we look for all numbers that make either inequality true.
Just as the United States is the union of all of the 50 states, the solution will be the union of all the numbers that make either inequality true. We solve compound inequalities using the same techniques we used to solve linear inequalities. The diastolic blood pressure measures the pressure while the heart is resting. Use a compound inequality to find the range of values for the width of the garden. Another way to graph the solution of is to graph both the solution of and the solution of We would then find the numbers that make both inequalities true as we did in previous examples. A compound inequality is made up of two inequalities connected by the word "and" or the word "or. Sometimes we have a compound inequality that can be written more concisely. This is a contradiction so there is no solution. Recall the problem solving strategies are to first read the problem and make sure all the words are understood. Our solution will be the numbers that are solutions to both inequalities known as the intersection of the two inequalities. Divide each part by three. In the following exercises, solve.
Ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. Is it a solution to the inequality in part (a)? Solve Applications with Compound Inequalities. Last, we will solve the compound inequality.
All the numbers that make both inequalities true are the solution to the compound inequality. We can see that the numbers between and are shaded on both of the first two graphs. Write a compound inequality that shows the range of numbers that Gregory might be thinking of. The usage is measured in the number of hundred cubic feet (hcf) the property owner uses. Solve the inequality. For example, the following are compound inequalities. Before you get started, take this readiness quiz. Learning Objectives. Access this online resource for additional instruction and practice with solving compound inequalities.
For the compound inequality and 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. Ⓐ Let x be your BMI. Add 7 to all three parts.
Then, identify what we are looking for and assign a variable to represent it. Graph the solution and write the solution in interval notation: or. We will use the same problem solving strategy that we used to solve linear equation and inequality applications. Then graph the numbers that make either inequality true. Let the number of hcf he can use. Name what we are looking for. The final graph will show all the numbers that make both inequalities true—the numbers shaded on both of the first two graphs.
Blood Pressure A person's blood pressure is measured with two numbers. Body Mass Index (BMI) is a measure of body fat is determined using your height and weight. There are no numbers that make both inequalities true. To find the solution of the compound inequality, we look at the graphs of each inequality, find the numbers that belong to either graph and put all those numbers together. In interval notation. Five more than three times her number is between 2 and 32. Penelope is playing a number game with her sister June. Ⓐ answers vary ⓑ answers vary. Answer the question. Therefore, it is be shaded on the solution graph.
32 per hcf for Conservation Usage. Graph each solution. To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement. What steps will you take to improve? Translate to an inequality. Make both inequalities. Consider how the intersection of two streets—the part where the streets overlap—belongs to both streets.
Elouise is creating a rectangular garden in her back yard. It is equivalent to and. 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. We solve each inequality separately and then consider the two solutions. Graph the numbers that. Research and then write the compound inequality to show the BMI range for you to be considered normal weight.
How many hcf can the owner use if she wants her usage to stay in the conservation range? The two forms are equivalent. The length of the garden is 12 feet.