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2.8 - Linear Inequalities
Algebra 2
Warm-Up:
Solve each inequality:
1.
x
2
3
2. 5(3 + x) < 3(x – 6)
Solve each equation for y:
3. 3x  4 y  5 ___________
4. 10 x  5 y  15
5. 6 y  10  2 x __________
6. 12 x  10  4 y
_______________________________________________________________________________________
Graphing Linear Inequalities:
1. Solve the inequality for y.
2. Graph the line as if the inequality were an equals sign (the slope is attached to x and the constant is
the y-intercept).
3. For < or > , the line needs to be dashed. For  or  , the line needs to be solid.
4. If the sign is < or  , shade the region BELOW the line. If the sign is > or  , shade the region ABOVE
the line.
5. To check your work, choose a point in the shaded region and plug it into the inequality.
Graph each linear inequality. Then, choose a point to check your work.
1. y ≥ 3x + 1
2. y < 5x + 2
3. y > 6x + 2
4. 2x + y ≤ -2
5. -2x – y ≥ 0
6. y > -3x – 4
7. y ≤
1
x3
2
9. x ≤ 2
8. y < -3
10. y ≤ 0
11. Michelle is planning a cookout. She has budgeted a maximum of $20 for hamburgers and hot dogs.
Hamburgers cost $3 per pound, and hot dogs cost $2 per pound.
a. Write an inequality to describe the possible number of pounds of meat she can purchase (let x =
pounds of hamburger and y = pounds of hot dogs).
b. Solve for y and graph the inequality.
c. Can Michelle afford to buy 5 pounds of hamburger?
How can you tell?
12. A pizza shop has 300 pounds of dough. A small pizza uses 12 ounces of dough and a large pizza uses 18
ounces of dough. What are the possible numbers of small and large pizzas that can be made?
a. Write and graph an inequality describing this situation.
b. Give three possible solutions to this problem.
Recap!
Tell whether the given ordered pair is a solution of the inequality.
1. x  7 ; (0, 10)
2. y  2 x  4 ; (-1, 8)
3. 2 x  y  3 ; (2, -2)
4. y 
2
x  2 ; (0, 0)
3
Graph each inequality.
3
x 1
4
5.  2 y  8
6. y 
7. 3x  y  2
8. 2 x  5 y  10