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Algebra 1 6-5 Guided Practice: Linear Inequalities

By Matt Richardson
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Last updated about 2 years ago
16 Questions
10
1.
Solve It! You are buying paperback and hardcover books at a book sale. You can spend at most $20.


What are the possible combinations of paperback and hardcover books that you can buy? Categorize each combination of books in the left column appropriately.
  • 8 paperbacks and no hardcovers
  • 1 paperbacks and 4 hardcovers
  • 3 paperbacks and 2 hardcovers
  • 4 hardcovers and no paperbacks
  • 3 hardcovers and 4 paperbacks
  • Can afford
  • Can not afford
10
2.
Take Note: Define linear inequality in two variables.
10
3.
Take Note: Provide an example of a linear inequality in two variables.
10
4.
Take Note: What is a solution of an inequality in two variables?
5
5.
Problem 1 Got It?
5
6.
Problem 1 Got It?
10
7.
Take Note: Graph two intersecting linear inequalities in two variables following the guidelines below.


One should contain < and the other should contain ≥.
You can type >= to create the ≥ symbol in most math input tools.
As you graph, notice the effects of the inequality symbols on the boundary lines and shading.
Zoom and pan your graph to establish an appropriate viewing window that includes the point of intersection.
10
8.
Take Note: Consider graphing a linear inequality in two variables that is written in slope-intercept form.

Place each inequality symbol from the left column below into two categories. One to describe its graph's boundary line (dashed or solid) and one to describe its graph's shaded half-plane relative to the boundary line (above or below).
  • <
  • >
  • \leq
  • \geq
  • SOLID boundary line
  • DASHED boundary line
  • Shaded half-plane ABOVE the boundary line
  • Shaded half-plane BELOW the boundary line
10
9.
Problem 2 Got It? What is the graph of the inequality below?
A.REI.12
10
10.
Problem 2 Got It? Of the 10 points added to the graph, which represent solutions of the inequality?
Select all that apply.
10
11.
Take Note: Consider the inequalities in the left column below.


Place each inequality into two categories. One to describe its graph's boundary line (vertical or horizontal) and the other to describe its graph's shaded half-plane relative to the boundary line (left, right, above, or below).
  • y\leq\pi
  • x\geq-\frac{9}{5}
  • y>3.5
  • x<7
  • SOLID boundary line
  • DASHED boundary line
  • Shaded half-plane ABOVE the boundary line
  • Shaded half-plane BELOW the boundary line
  • Shaded half-plane to the LEFT of the boundary line
  • Shaded half-plane to the RIGHT of the boundary line
10
12.
Problem 3 Got It? What is the graph of the inequality?
A.REI.12
10
13.
Problem 3 Got It? What is the graph of the inequality?
A.REI.12
20
14.
Problem 4 Got It? For a party, you can spend no more than $12 on nuts. Peanuts cost $2/lb. Cashews cost $4/lb. Graph the inequality. Show relevant graph detail. What are three possible combinations of peanuts and cashews you can buy?

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.
A.REI.12
10
15.
Problem 5 Got It?
A.REI.12
10
16.
Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?