Solving Inequalities
Solve: 3x - 7 < 5
x < 4
What is the solution to the system: y = 2x + 1 and y = -x + 4?
(1, 3)
What kind of line is used for y < 2x + 1?
A dashed line
You make $2 per cookie. Write an inequality for earning at least $20.
2c ≥ 20
What does a point on the shaded region represent in real life?
A possible solution
Solve: -2x + 5 ≥ 11
x ≤ -3
How many solutions does a system of parallel lines have?
Answer: None
Which side of the line do you shade for y > -x + 3?
Above
A movie ticket costs $8. You have $50. What’s the max tickets you can buy?
8t ≤ 50 → t ≤ 6
Give a real-world example of a linear inequality.
Any real world example is right
True or False: The inequality x > 2 is shaded to the left.
Answer: False
Solve by substitution: y = x + 2 and 2x - y = 4
Answer: (2, 4)
Graph y ≥ 2x - 4. What’s the boundary line?
y = 2x - 4, solid line
A movie ticket costs $8. You have $50. What’s the max tickets you can buy?
8t ≤ 50 → t ≤ 6
Which math representation helps compare two products?
A graph or table
Solve : 2x + 4 > 10
x<3
What does one solution mean for a system of equations?
Answer: The lines intersect at one point.
What does the shaded region represent?
All the solutions to the inequality
You work 3 hours for $12/hour. You want at least $36. Write an inequality.
12h ≥ 36
Why would a dashed line be used in a real-life model?
To show values that are not included
Solve: 4(x - 2) ≤ 2x + 6
x ≤ 7
Solve the system by elimination: 3x + 2y = 12 and -3x + y = 3
(0, 3)
What happens if two inequalities don’t overlap when graphed?
No solution to the system
You need at least 90 points to pass. You’ve earned 75. Write inequality.
x + 75 ≥ 90 → x ≥ 15
You’re creating a budget for school supplies. You want to spend at most $50. Pencils cost $0.50 and notebooks cost $2. Write an inequality.
0.5x+2y<_ 50