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