Some of the solutions are 2, 3, 3. Since it is impossible to list all of the solutions, a system is needed that allows a clear communication of this infinite set.

Student View Task Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can only carry pounds of people and gear for safety reasons.

Assume the average weight of a person is pounds. Each group will require lbs of gear for the boat plus 10 lbs of gear for each person. Create an inequality describing the restrictions on the number of people possible in a rented boat.

Graph the solution set.

Several groups of people wish to rent a boat. Group 1 has 4 people. Group 2 has 5 people. Group 3 has 8 people.

Which of the groups, if any, can safely rent a boat? What is the maximum number of people that may rent a boat?

IM Commentary This task is the second in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically. The progression of the content standards is 6.

This particular task could be used for instruction or assessment. To see an annotated version of this and other Illustrative Mathematics tasks as well as other Common Core aligned resources, visit Achieve the Core. We also know that the total weight cannot exceed pounds.

So we arrive at the following inequality:The inequalities are graphed separately on the same graph, and the solution for the system is the common shaded region between all the inequalities in the system.

One linear inequality in two variables divides the plane into two half-planes. Since the inequality symbol is. How Do You Graph an Inequality or an Infinite Set on a Number Line? Number lines are really useful in visualizing an inequality or a set.

In . Solve the inequality x > 6x - 10 and write a description of the graph. Show all work Subtracting x from both sides does not change the inequality sign direction. 0 > 5x - 10 Add 10 to both sides 5x 10 Divide both sides by 5. x 2. The solutions of an inequality can be represented on a number line which is shown in the following examples.

Example: Represent the solution set of inequality x + 4 ≤ 8, where ‘ x ’ is a whole number.

minimum height above the ground are shown. Write and graph a compound inequality that describes the possible • Write a compound inequality that describes the possible temperatures (in degrees Fahrenheit) at a Lesson Quiz 1.

Solve x + 4 3. Graph your solution.

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