DAY 8 – LINEAR
INEQUALITIES
Jason collects card-game packages. The cost
of each card packages for Game A is $3, and
the cost of each card packages for Game B is
$2. How many card packages for each game
Jason buy? The answer to this question can
be found using the graph of a linear
inequality.
GRAPHING A LINEAR INEQUALITY
1. Let 𝑥 represent the number of card packages for
Game A, and let 𝑦 represent the number of card
packages for Game B. write an inequality to
represent the amount of money Jason can spend
each week on card packages.
𝟑𝐱 + 𝟐𝐲 ≤ 𝟏𝟐
2. Replace the inequality symbol with an equal
sign in the inequality you wrote in Step 1. Solve
for y, and graph the equation on a coordinate
plane. This line is called the boundary line of the
related inequality.
3. The following table shows you can use
substitution to find some points that satisfy
inequality. Copy and complete the table.
4. Which points in the table make inequality true?
Plot them on the graph you drew in Step 2.
𝟎, 𝟎 , 𝟏, 𝟏 , 𝟐, 𝟏 , 𝟐, 𝟐 , (𝟑, 𝟏)
5. Shade the region on the side of the line
containing the points you plotted in Step 4. What is
true about all of the points in this region?
They all make the inequality 𝟑𝒙 + 𝟐𝒚 ≤ 𝟏𝟐 true.
6. Are all of the points in the shaded region
solutions to the inequality? What are the
reasonable domain and range for this real-world
situation?
Yes; 𝟎 ≤ 𝒙 ≤ 𝟒; 𝟎 ≤ 𝒚 ≤ 𝟔
7. Can you list 𝑎𝑙𝑙 of the possible numbers of card
packages from Games A and B That Jason can buy
in one week? Explain.
Why is the ordered pair
1
2 ,
2
1
1
2
a solution to the
inequality but not a real answer to the problem in
Exploration 1?
These coordinates produce a true statement
when substituted in 𝟑𝒙 + 𝟐𝒚 ≤ 𝟏𝟐, but this is
not a solution because you cannot buy partial
packages.
A GREATER- THAN INEQUALITY
8. What is the equation of the boundary line for
the inequality 𝑦 < 2𝑥 − 4?
𝒚 = 𝟐𝒙 − 𝟒
9. Graph the boundary line. If an inequality
contains the symbol < or >, the boundary line
𝑖𝑠 𝑛𝑜𝑡 part of the graph and is shown as a 𝑑𝑎𝑠ℎ𝑒𝑑
line. If the inequality contains the symbol ≤ or ≥,
the boundary line is part of the graph and is
shown as a 𝑠𝑜𝑙𝑖𝑑 line. Is the boundary line in the
inequality 𝑦 > 2𝑥 − 4 solid or dashed?
9. Dashed
10. Copy and complete the following table to find
points that make the inequality true.
11. Plot the points from the table that satisfy the
inequality. Do the points lie above or below the
boundary line? Shade the region containing these
points.
10. Copy and complete the following table to find
points that make the inequality true.
11. Plot the points from the table that satisfy the
inequality. Do the points lie above or below the
boundary line? Shade the region containing these
points.
11.
12. Explain how to use the inequality to
determine which side of the line to shade.
Substitute the coordinates of different
points into the inequality. The points
that make the inequality true will all
be on the side of the boundary line that
is to be shaded.