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Five more than three times her number is between 2 and 32. A double inequality is a compound inequality such as. Now that we know how to solve linear inequalities, the next step is to look at 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. To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement. The final graph will show all the numbers that make both inequalities true—the numbers shaded on both of the first two graphs. Solve Applications with Compound Inequalities. 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. This is a contradiction so there is no solution. 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. The homeowner can use 16–40 hcf and still fall within the "normal usage" billing range. Access this online resource for additional instruction and practice with solving compound inequalities. Solving for compound inequalities. 32 per hcf for Conservation Usage.

5-4 Practice Solving Compound Inequalities

Ⓑ What does this checklist tell you about your mastery of this section? Add 7 to all three parts. Blood Pressure A person's blood pressure is measured with two numbers. Solve the inequality.

Translate to an inequality. Then graph the numbers that make either inequality true. During the winter, a property owner will pay? Penelope is thinking of a number and wants June to guess it. What steps will you take to improve?

Solving For Compound Inequalities

The number of hcf he can use and stay in the "normal usage" billing range. Gregory is thinking of a number and he wants his sister Lauren to guess the number. How to solve a compound inequality with "or". In interval notation. Research and then write the compound inequality that shows you what a normal diastolic blood pressure should be for someone your age. Use a compound inequality to find the range of values for the width of the garden. 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. Rules for solving compound inequalities. The solution covers all real numbers. All the numbers that make both inequalities true are the solution to the compound inequality. Write the solution in interval notation. 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. Then, identify what we are looking for and assign a variable to represent it.

The length of the garden is 12 feet. Ⓑ Let y be your diastolic blood pressure. For example, the following are compound inequalities. Make both inequalities. Our solution will be the numbers that are solutions to both inequalities known as the intersection of the two inequalities. Penelope is playing a number game with her sister June. Last, we will solve the compound inequality. We can then graph the solution immediately as we did above. Next, restate the problem in one sentence to make it easy to translate into a compound inequality. Solving compound inequalities worksheet. The number two is shaded on both the first and second graphs.

Solving Compound Inequalities Worksheet

The usage is measured in the number of hundred cubic feet (hcf) the property owner uses. Write a compound inequality that shows the range of numbers that Gregory might be thinking of. 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. Body Mass Index (BMI) is a measure of body fat is determined using your height and weight. 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. We solve each inequality separately and then consider the two solutions. Graph the numbers that. We then look for where the graphs "overlap".

Ⓐ answers vary ⓑ answers vary. There are different rates for Conservation Usage, Normal Usage and Excessive Usage. Ⓐ Let x be your BMI. This is how we will show our solution in the next examples. It is equivalent to and. The two forms are equivalent. Graph the solution and write the solution in interval notation: or. Therefore, it is be shaded on the solution graph. Practice Makes Perfect. Let's start with the compound inequalities with "and. " A compound inequality is made up of two inequalities connected by the word "and" or the word "or. 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. To solve a compound inequality with the word "or, " we look for all numbers that make either inequality true.

Rules For Solving Compound Inequalities

The bill for Conservation Usage would be between or equal to? 54 times the number of hcf he uses or|. Situations in the real world also involve compound inequalities. This graph shows the solution to the compound inequality. Compound inequality. Before you get started, take this readiness quiz. Ⓑ Research a BMI calculator and determine your BMI. The systolic blood pressure measures the pressure of the blood on the arteries as the heart beats. For the compound inequality and we graph each inequality. In the following exercises, solve.

The numbers that are shaded on both graphs, will be shaded on the graph of the solution of the compound inequality. The perimeter of the garden must be at least 36 feet and no more than 48 feet. Explain the steps for solving the compound inequality or. Answer the question. There are no numbers that make both inequalities true. The diastolic blood pressure measures the pressure while the heart is resting. Sometimes we have a compound inequality that can be written more concisely. Solve Compound Inequalities with "and".

We can see that the numbers between and are shaded on both of the first two graphs. Learning Objectives. 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. How many hcf can the owner use if she wants her usage to stay in the conservation range? His first clue is that six less than twice his number is between four and forty-two. Graph the solution and write the solution in interval notation: Solve Compound Inequalities with "or". We will use the same problem solving strategy that we used to solve linear equation and inequality applications. By the end of this section, you will be able to: - Solve compound inequalities with "and".

For example, and can be written simply as and then we call it a double inequality. Let the number of hcf he can use.