Basic Equations and Solutions
Multi-step Equations
Ratios and Proportions
Rates and Scale Drawings
100
List the 4 basic operations and their inverses
Addition - Subtraction
Subtraction - Addition
Multiplication - Division
Division - Multiplication
100
List the three different solution types
One Solution
No Solution
Many Solutions
100
For the rate below, if you want to multiply by the unit rate 1min:60sec, which value should be in the numerator?
(15ft)/(sec)
60 sec, to cancel the sec in the denominator
100
List 3 examples of scale drawings in the real world
See Answers
200
How do you choose which side to be your "variable side" in an equation with variables on both sides?
Create an Example
Whichever side has "more variables"
3x - 1 = 64x - 19 (right side is variable side)
200
What is the first step in solving the following equation?
4(x + 1) = 24
Distribute the 4
200
Solve the following proportion
k/5=21/15
k = 7
200
Use the Order of Operations to simplify the following expression:
9
300
solve the following equation for r
-5 + r = -17
r = -12
300
Solve the following equation for y:
7(y -3)+10 = 66
y = 11
300
Solve the proportion
4/(m-8)=8/2
m=9
300
List the proper steps (like we've done in class, do not solve) to convert 50 yards per day into feet per hour.
(50yd)/(1 day) * (1 day)/(24 hours) * (3ft)/(1yd)
400
Solve the following equation for b
-4b = 12
b = -3
400
Determine whether the following has one solution, no solution, or many solutions:
4(x + 5) -3 = 4x + 17
Many Solutions
400
A case of 24 tennis balls weighs 3 pounds. How much would a shipment of 2560 tennis balls weigh?
320 pounds
400
A map of Connecticut is drawn to the following scale:
2in:35 miles
If Greenwich and Wtonington are 105 miles apart from each other, how far apart do they appear on the map?
6in
500
Solve the following equation for x
3(x + 2) = 15
x = 3
500
Solve the following equation for v
-7(4v+7)=3+4(-4-6v)
v = -9
500
Solve the proportion
2/8=(n+4)/(n-4)
n=-20/3
500
A car rides slowly at 12 miles per hour. Convert this rate into feet per second
(hint: 5,280ft = 1 mile)
17.6 ft/sec
600
State the inverse operation for each of the following operations
x^2
x^3
"Square Rooting"
"Cube Rooting"
600
Solve the following equation of x
-2(4-3x)+3x=27+2x
No Solution
600
Serena paid a tax of $288 on a house that cost $48,000. Find how much tax would be paid on a $59,000 house.
$354
600
Using the scale drawing below, calculate the actual perimeter of the apartment in ft.
108 ft