Inequalities
Solve and graph:
x−7>3
MUST GRAPH
x−7>3
Add 7 to both sides → x>10x
Graph: open circle at 10, shade right
A circle has a diameter of 10 units. What is the area? Use 3.14 for pi. You may use Desmos.
Radius = 102=5\frac{10}{2} = 5210=5
Use area formula:
Final Answer: 78.5 square units
5+7×3−4÷2
Multiply/divide first:
7×3=217 \times 3 = 217×3=21
4÷2=24 \div 2 = 24÷2=2
Now:
5+21−2=245 + 21 - 2 = 245+21−2=24
Final Answer: 24
Original = 4, New = 3/2
3/8
−3x+5=20
Subtract 5:
−3x=15
Final Answer: -5
-3x>15
Divide by -3 → x< 5x
Graph: closed circle at 5, shade left
A circle has a radius of 6 units. What is the circumference? Use 3.14 for pi. You may use Desmos.
Final Answer: 37.68 units
1. What's the Percent Change Formula?
2.The price of a hoodie was $40. It is now $50. What is the percent change? Is it an increase or decrease?
Use Desmos :)
1.New-Old/Old times 100!!
25% increase
Original = 6, New = 9/4
3/8
(x/-4)−6=2
Final Answer: -32
−3x+6<18
−3x+6<18
Subtract 6 → −3x<12-3x < 12−3x<12
Divide by -3 (flip inequality!) → x>−4x > -4x>−4
Graph: open circle at -4, shade right
A cylinder has a diameter of 8 units and a height of 10 units. What is the volume? Use 3.14 for pi. You may use Desmos.
Step 1: Find radius
Diameter = 8 → Radius = 4
Final Answer: 502.4 cubic units
A pair of shoes was originally $80. The price is now $60. What is the percent change? Is it an increase or decrease?
25% decrease
Original = 3, New = 7/6
7/18
2/3x+(−4)=10
Final Answer: 21
(x/-2)≥4
Multiply by -2 (flip inequality!) → x≤−8x \le -8x≤−8
Graph: closed circle at -8, shade left
A rectangular prism has a volume of 3,600 cubic units, a length of 25 units, and a height of 12 units. What is the width?
You may use Desmos.
Final Answer: 12 units
Write the prime factorization of 84.
Break 84 down step by step:
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
Now list all prime factors:
Final Answer:
2^2×3×7
Original = 5, New = 11/4
11/20
−2x+9=−11
x=10
Solve and graph:
(x−4)/−3 ≤2
Multiply by -3 (flip inequality!):
Add 4:
x≥−2
Graph: closed circle at -2, shade right
A circle has an area of 25π square units. What is the circumference?
Final Answer: 10π
Write the prime factorization of 168.
168=2×2×2×3×7
2^3×3×7
Original side length = 7
Scaled image side length = 5/3
5/21
−3/5x−7=8
-25