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EWG JH Algebra 1 Unit 7 Inequalities Test

By Bethany Mooney
Last updated over 4 years ago
34 Questions
Note from the author:
This assessment is modeled after the EWG HS Algebra 1 Linear Unit 2.2 unit on inequalities.
For questions 1-4, write an inequality that corresponds to each statement:
1.

A weight of at least 70 lbs

2.

A temperature below

3.

A height above 48 inches but no more than 78 inches

4.

Children under 10 or seniors 55 and older get a reduced price. Let a = ages that get a reduced price.

For items 5-8, solve each inequality and graph its solution. Circle your final solution and graph it at the bottom of your work.
5.

6.

7.

8.

For items 9-14, write and solve an inequality to answer each question. Remember to label your answers.
9.

Five times a number, decreased by 4 is less than seven times the same number.
Write the inequality that models the statement exactly as it is expressed above.

10.

What is the smallest integer the number in question 9 above could be?

11.

Skate Land charges a $75 facility usage fee for a birthday party rental and $7 per person. The cake for the party has already been ordered and costs $47. The Smith family wants to spend less than $250 for the entire birthday party. Write an inequality to model this situation. Let p = the number of people invited.

12.

What is the maximum number of guests that can be invited to the party at Skate Land?

13.

The sum of three times a number and two lies between 8 and 20. Write an inequality to model this situation. Let n = the number.

14.

What integers can the number be in problem 13 above?

Graph each linear inequality.
15.

Graph

16.

Graph

17.

The shaded region represents the solution to a system of inequalities. Select the two inequalities that make up the system.

18.

The shaded region represents the solution to a system of inequalities. Select the two inequalities that make up the system.

19.

The shaded region represents the solution to a system of inequalities. Select the two inequalities that make up the system.

20.

Select the points that are solutions to the system.


Use the graph to answer the following 2 questions.
21.

Write a system of inequalities to represent the graph.

22.

Which region represents the solution to the system of inequalities?

23.

Explain what your answer to item #22 means.

24.

Opal makes $15 per hour working for a photographer. She also coaches a competitive soccer team for $10 per hour. Opal needs to earn at least $90 per week, but she does not want to work more than 20 hours per week.
Write a system of inequalities to model the situation.

Let x represent the number of hours worked as a photographer.
Let y represent the number of hours coaching.
Use <= and >= to represent

25.

Graph the system of inequalities you wrote in item #24 above. Be sure to label the axes appropriately and show numbering.
Each boundary line must have two points plotted and the correct type of line (solid or dashed). Shade only the solution area.

26.

Determine which of the following answers would be solutions to Opal's situation. Select all that apply.

Solve each absolute value inequality and graph your solution. Show your work, circle the final solution and graph it.
27.

28.

29.

Write an inequality that meets the following criteria.
30.

The boundary line has a slope of 4 and a y-intercept of (0,5). The points (1, 9) and (2, 7) are solutions to the inequality.

31.

The boundary line is a horizontal line and the y-intercept is (0, -2). The point (1,10) is a solution. The point (1,-2) is not a solution.

32.

The boundary line is dashed, has a slope of -3, and passes through (-2,10). The point (1,-5) is in the shaded region.

33.

Write and graph a system of inequalities that models the following situation.
The owner of Wil's Fish Market orders cod and tuna. He wants to buy at least 40 pounds of fish, but cannot spend more than $400. Cod is $5 per pound and tuna is $8 per pound.
Let x = amound of cod (in pounds)

34.

Which of the following combinations of cod and tuna can Wil buy?