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