systems of linear inequalities
systems of linear inequalities
solutions to systems of linear inequalities
linear inequalities
Solving Inequalities
100
The school store must sell at least 18 notebooks to qualify for a special discount. Let n represent the number of notebooks sold.
Write an inequality that represents the situation.
n >= 18
100
Graph the system of inequalities and provide 2 possible solutions:
y > x
y < 2x
Answers vary
100
Without using Desmos
Show a graph for this system of inequalities:
x >= 0
y <= 3
Parris show capture 6
100
BONUS: How many days until Thanksgiving? (not including today or Thanksgiving Day)
29
100
Solve for x and graph on a number line:
x/3 + 5 < 11
x<18
200
A class has $120 available for a field trip. Transportation costs $30, and admission costs $15 per student. Let s represent the number of students.
Write and solve an inequality to find the maximum number of students who can attend.
30 + 15s ≤ 120 → 15s ≤ 90 → s ≤ 6. Maximum: 6 students.
200
A solid line is used when...?
less than or equal to OR greater than or equal to
200
BONUS: How many children does Mrs. Beigel have?
3
200
Carrie wants to spend at least 3 hours at the beach (X)
Write an inequality to show this situation
x >= 3
200
Solve for x and graph on a number line
-4x + 7 >31
x<18
300
A school sells adult tickets for $8 and student tickets for $5. A group wants to buy at least 12 tickets while spending no more than $80. Let a represent adult tickets and s represent student tickets.
Write a system of inequalities representing both conditions.
a + s ≥ 12 and 8a + 5s ≤ 80. For a real-world ticket count, a ≥ 0 and s ≥ 0, with whole-number values.
300
Is (0,5) a possible solution to the system of inequalities? Why or why not?
Yes - it falls on a solid line in the double shaded area
300
Explain what it means for a point to be a solution in the context of a system of linear inequalities.
Answers vary: for it to be a solution, it needs to make both inequalities true and fall in the area where both sets of inequalities shading overlaps
300
What is the solution to a system of linear inequalities when both lines have the same slope with opposite shading?
no solution
300
Jordan rents a bike that costs a $3.50 fee plus $2.25 for each mile ridden. Jordan has $20 to spend. Write and solve an inequality to find the number of miles m Jordan can ride.
m<=22/3 or 7.33
400
BONUS: What town does Mrs. Beigel live in?
Dunstable
400
Is the point (0,4) part of the solution set?
No - it falls on a dotted line
400
How could you determine if a point is a solution without graphing?
Answers vary: the x and y of the point should satisfy both equations and make them true
400
How can you verify the solution obtained from graphing a system of linear equations?
Answers vary: Plug in the x and the y values. Both equations should be made "true."
400
Solve the inequality for x.
-2/3 x + 4 >10
x < -9
500
A food bank prepares fruit boxes for delivery. Each apple box weighs 3 pounds and each orange box weighs 5 pounds. A truck can carry no more than 40 pounds, and the food bank must deliver at least 10 boxes. Let a represent apple boxes and o represent orange boxes. A volunteer proposes delivering 4 apple boxes and 6 orange boxes.
Write a system of inequalities for the situation.
a + o ≥ 10 and 3a + 5o ≤ 40. Use nonnegative whole-number values for a and o.
500
List the two inequalities that make up this system of inequalities.
y <= 5
x > 3
500
What is a/the solution to this set of inequalities?
y >-2x +1
y - 1 > -2x
infinitely many solutions
500
What are the equations for this system of linear equations?
y = 4x + 2
y= -2x+3
500
Solve the inequality for x:
3/4 - x/2 > x/4 + 3
x<-3