Solving, Graphing, Writing Interval Notation
"or" inequalities
"and" inequalities
word problems
mx+b word problems
100
Graph and write the interval notation:
x ≤ 7
Interval Notation: _____
(-∞ , 7]
100
graph and write the interval notation:
x<4 or x>8
Interval Notation: __________________________
(-∞ , 4) U (8, ∞)
100
-2 < x ≤ 5
Interval Notation: __________________________
Interval Notation: (-2, 5]
100
Set up AND solve:
Six more than twice a number is less than 20.
2x + 6 < 20
2x < 14
x < 7
100
A class is planning a trip that costs $32 per student for transportation. The school has already contributed $160. The total budget is no more than $800.
What is the greatest number of students who can attend?
________ students
32x + 160 ≤ 800
32x ≤ 640
x ≤ 20
Answer: 20 students
200
Graph and write the interval notation:
-10 < x ≤ 4
Interval Notation: __________________________
(-10, 4]
200
Solve, then graph and write the interval notation: 2x+4 ≤ 12 or 3x - 1>14
Interval Notation: __________________________
x ≤ 4 or x > 5
(-∞ , 4] U (5, ∞)
200
-2x + 4 ≥ 8 AND x + 3 < 5
Interval Notation: __________________________
-2 ≤ x < 2
Interval Notation: [-2, 2)
200
Set up AND solve:
Eight more than five times a number is greater than 33.
5x + 8 > 33
5x > 25
x > 5
200
A school club is selling T-shirts for $15 each. The club already has $75. It wants to raise at least $300 total.
How many T-shirts does the club need to sell?
________ T-shirts
75 + 15x ≥ 300
15x ≥ 225
x ≥ 15
Answer: 15 T-shirts
300
Graph and write the interval notation:
x ≤ -5 or x ≥ 9
Interval Notation: __________________________
(-∞ , -5] U [9, ∞)
300
Solve, then graph and write the interval notation: -2x+6>12 or x - 5 ≥ 3
Interval Notation: __________________________
x < -3 or x ≥ 8
(-∞, -3) U [8, ∞)
300
-5 ≤ 3x + 1 < 7
Interval Notation: __________________________
-2 ≤ x < 2
Interval Notation: [-2, 2)
300
Set up AND solve:
Twice a number decreased by 9 is at most 15.
2x - 9 ≤ 15
2x ≤ 24
x ≤ 12
300
A bowling alley charges $6 per game plus a one-time shoe rental fee of $4. Jordan has $40 to spend.
What is the greatest number of games Jordan can play?
________ games
6x + 4 ≤ 40
6x ≤ 36
x ≤ 6
Answer: 6 games
400
Solve, then graph and write the interval notation:
-2x > 10
Interval Notation: __________________________
x<-5
(-∞ , -5)
400
-2x + 7 < x - 8 OR 4x + 3 < 2x + 11
Interval Notation: __________________________
x > 5 or x < 4
(-∞, 4) ∪ (5, ∞)
400
-7 ≤ -2x + 3 < 11
Interval Notation: __________________________
-4 < x ≤ 5
Interval Notation: (-4, 5]
400
Set up AND solve:
Three times a number increased by 5 is at least 29.
3x + 5 ≥ 29
3x ≥ 24
x ≥ 8
400
Diego is saving money for a video game system that costs $350. He already has $50 and earns $25 per week doing chores.
How many weeks does he need to save to have enough money?
________ weeks
50 + 25x ≥ 350
25x ≥ 300
x ≥ 12
Answer: 12 weeks
500
2x+4 ≥ 14
Interval Notation: __________________________
x ≥ 5
[5, ∞)
500
Solve, then graph and write the interval notation: 4x-7>2x+5 or 3x+8≥5x-2
Interval Notation: __________________________
x>6 or x ≤ 5
(-∞, 5] U (6, ∞)
500
-8 ≤ 2(3x - 1) < 16
Interval Notation: __________________________
-1 ≤ x < 3
Interval Notation: [-1, 3)
500
Set up AND solve:
Seven less than four times a number is no more than 21.
4x - 7 ≤ 21
4x ≤ 28
x ≤ 7
500
Emma is buying movie tickets. Each ticket costs $12. She has already spent $8 on snacks. She has $50 total to spend.
How many tickets can she buy?
________ tickets
12x + 8 ≤ 50
12x ≤ 42
x ≤ 3.5
Answer: 3 tickets