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To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement. The usage is measured in the number of hundred cubic feet (hcf) the property owner uses. How to solve a compound inequality with "or". 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. How many hcf will he be allowed to use if he wants his usage to stay in the normal range? Let the number of hcf he can use. Solving compound inequalities pdf. Therefore, it is be shaded on the solution graph. To solve a compound inequality with the word "or, " we look for all numbers that make either inequality true. Then, identify what we are looking for and assign a variable to represent it. Is it a solution to the inequality in part (a)? Solve Compound Inequalities with "and". 32 per hcf for Conservation Usage.
5-4 Practice Solving Compound Inequalities Answer Key
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. By the end of this section, you will be able to: - Solve compound inequalities with "and". Divide each part by three. There are different rates for Conservation Usage, Normal Usage and Excessive Usage. Now that we know how to solve linear inequalities, the next step is to look at compound inequalities. The systolic blood pressure measures the pressure of the blood on the arteries as the heart beats. Make both inequalities. Research and then write the compound inequality to show the BMI range for you to be considered normal weight. How to solve compound inequalities with and. The solution covers all real numbers. The final graph will show all the numbers that make both inequalities true—the numbers shaded on both of the first two graphs.
Recall the problem solving strategies are to first read the problem and make sure all the words are understood. The number two is shaded on both the first and second graphs. The bill for Conservation Usage would be between or equal to? Solving Linear Equations. 5-4 practice solving compound inequalities answer key. Solve Applications with Compound Inequalities. 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.How To Solve Compound Inequalities With And
We then look for where the graphs "overlap". Ⓑ What does this checklist tell you about your mastery of this section? Blood Pressure A person's blood pressure is measured with two numbers. The diastolic blood pressure measures the pressure while the heart is resting. Ⓑ Research a BMI calculator and determine your BMI. It is equivalent to and. Let's start with the compound inequalities with "and. " Translate to an inequality. Solve the inequality. 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. Practice Makes Perfect. Graph the numbers that. 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. The number of hcf he can use and stay in the "normal usage" billing range.54 times the number of hcf he uses or|. 54 per hcf for Normal Usage. We will use the same problem solving strategy that we used to solve linear equation and inequality applications. 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. Write the solution in interval notation. A compound inequality is made up of two inequalities connected by the word "and" or the word "or. Research and then write the compound inequality that shows you what a normal diastolic blood pressure should be for someone your age. Consider how the intersection of two streets—the part where the streets overlap—belongs to both streets. His first clue is that six less than twice his number is between four and forty-two. The homeowner can use 16–40 hcf and still fall within the "normal usage" billing range.
Solving For Compound Inequalities
What steps will you take to improve? We can then graph the solution immediately as we did above. This graph shows the solution to the compound inequality. Explain the steps for solving the compound inequality or. Ⓐ answers vary ⓑ answers vary. The perimeter of the garden must be at least 36 feet and no more than 48 feet. This is a contradiction so there is no solution. Graph the solution and write the solution in interval notation: Solve Compound Inequalities with "or". Answer the question. Graph the solution and write the solution in interval notation: or. Add 7 to all three parts.
Graph each solution. Five more than three times her number is between 2 and 32. Our solution will be the numbers that are solutions to both inequalities known as the intersection of the two inequalities. In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. All the numbers that make both inequalities true are the solution to the compound inequality. The two forms are equivalent. Name what we are looking for.
Solving Compound Inequalities Pdf
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. Due to the drought in California, many communities now have tiered water rates. Elouise is creating a rectangular garden in her back yard. Penelope is playing a number game with her sister June. Last, we will solve the compound inequality. Ⓐ Let x be your BMI. This is how we will show our solution in the next examples. In interval notation.
For example, the following are compound inequalities. Compound inequality. We solve each inequality separately and then consider the two solutions. 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. Make either inequality.
Gregory is thinking of a number and he wants his sister Lauren to guess the number. Ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. There are no numbers that make both inequalities true. Sometimes we have a compound inequality that can be written more concisely. In the following exercises, solve.