Next, restate the problem in one sentence to make it easy to translate into a compound inequality. The usage is measured in the number of hundred cubic feet (hcf) the property owner uses. To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement. Now that we know how to solve linear inequalities, the next step is to look at compound inequalities. A compound inequality is made up of two inequalities connected by the word "and" or the word "or. Access this online resource for additional instruction and practice with solving compound inequalities. The diastolic blood pressure measures the pressure while the heart is resting. There are different rates for Conservation Usage, Normal Usage and Excessive Usage. All the numbers that make both inequalities true are the solution to the compound inequality. Explain the steps for solving the compound inequality or. 54 per hcf for Normal Usage.
5-4 Practice Solving Compound Inequalities
Then graph the numbers that make either inequality true. The perimeter of the garden must be at least 36 feet and no more than 48 feet. Penelope is playing a number game with her sister June. There are no numbers that make both inequalities true. In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. Last, we will solve the compound inequality. Solve Compound Inequalities with "and".
Compound Inequalities Practice Pdf
32 per hcf for Conservation Usage. We can see that the numbers between and are shaded on both of the first two graphs. 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. In the following exercises, solve. In your own words, explain the difference between the properties of equality and the properties of inequality. It is equivalent to and. Situations in the real world also involve compound inequalities. Then, identify what we are looking for and assign a variable to represent it. The two forms are equivalent. Research and then write the compound inequality to show the BMI range for you to be considered normal weight. Use a compound inequality to find the range of values for the width of the garden.
Solving Compound Inequalities Worksheet
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. Translate to an inequality. The number two is shaded on both the first and second graphs. 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. This graph shows the solution to the compound inequality. Graph each solution. Penelope is thinking of a number and wants June to guess it. By the end of this section, you will be able to: - Solve compound inequalities with "and". Solve the inequality. The numbers that are shaded on both graphs, will be shaded on the graph of the solution of the compound inequality. Learning Objectives. His first clue is that six less than twice his number is between four and forty-two. Ⓐ answers vary ⓑ answers vary.
5-4 Practice Solving Compound Inequalities Answers
We solve compound inequalities using the same techniques we used to solve linear inequalities. How many hcf will he be allowed to use if he wants his usage to stay in the normal range? Research and then write the compound inequality that shows you what a normal diastolic blood pressure should be for someone your age. How many hcf can the owner use if she wants her usage to stay in the conservation range? The length of the garden is 12 feet.
Rules For Solving Compound Inequalities
Make both inequalities. Before you get started, take this readiness quiz. 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. Graph the solution and write the solution in interval notation: or. 54 times the number of hcf he uses or|. Write a compound inequality that shows the range of numbers that Gregory might be thinking of. Compound inequality. The number of hcf he can use and stay in the "normal usage" billing range. We will use the same problem solving strategy that we used to solve linear equation and inequality applications. Sometimes we have a compound inequality that can be written more concisely. Let's start with the compound inequalities with "and. " Solving Linear Equations. Answer the question. Graph the numbers that.
Gregory is thinking of a number and he wants his sister Lauren to guess the number. For example, the following are compound inequalities. To solve a compound inequality with the word "or, " we look for all numbers that make either inequality true. The systolic blood pressure measures the pressure of the blood on the arteries as the heart beats. Ⓑ Let y be your diastolic blood pressure. Is it a solution to the inequality in part (a)? The homeowner can use 16–40 hcf and still fall within the "normal usage" billing range. Elouise is creating a rectangular garden in her back yard. A double inequality is a compound inequality such as. Our solution will be the numbers that are solutions to both inequalities known as the intersection of the two inequalities. 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. In interval notation. What steps will you take to improve? Let the number of hcf he can use.
Body Mass Index (BMI) is a measure of body fat is determined using your height and weight. We solve each inequality separately and then consider the two solutions. This is a contradiction so there is no solution. Therefore, it is be shaded on the solution graph. The bill for Conservation Usage would be between or equal to?
Divide each part by three. For the compound inequality and we graph each inequality. The final graph will show all the numbers that make both inequalities true—the numbers shaded on both of the first two graphs. Practice Makes Perfect.
During the winter, a property owner will pay? Add 7 to all three parts. Recall the problem solving strategies are to first read the problem and make sure all the words are understood.
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