Properties
Name the following property:
a + b = b + a
Commutative Property of Addition
Solve and graph:
3 - 3x < 27
x> -8
Solve:
|4x| = 16
x = 4, x = -4
u = 1 + 2a
a = (u - 1)/2
Three consecutive numbers have the sum of 159. What are those three numbers?
52, 53, 54
Name the following property
a(bc) = (ab)c
Associative Property of Multiplication
Solve and Graph:
3a - 5 > -35
a > -10
Solve :
|p+7| = 4
p = -3 , p = -11
Isolate x:
xm = p + n
x = (p+n)/m
The sum of 3 consecutive even integers = 258. What are the numbers?
84, 86, 88
Name the following property:
4 + 0 = 4
Identity Property of Addition
14 > (5+b)/2
b<23
Solve and Graph:
|6x + 6|> 42
x > 6 OR x < 8
Isolate a:
u = b + ak
a = (u - b)/k
One person joins a swim club that costs $253 to join and $4 per visit to go on the water slides. If you aren't a member, you have to pay $15 per visit. How many times would you need to visit the water slides to justify paying for membership?
23 visits
(1/2) x 2 = 1
Inverse Property of Multiplication
Graph and Solve:
-17 < -9 - n
n < 8
Solve:
|-2p - 2| < 4
Isolate a:
am = np
a = (np)/m
The average January temperature in a Canadian city is 1 degree F. The actual January temperature for that city may be about 5 degrees warmer or colder. Write an solve an absolute deviation equation to find the minimum and maximum temperatures.
t = 6 F (maximum)
Name the Property:
6(0) = 0
Multiplication Property of Zero
Graph and solve:
5/3b - 1/10 < 47/30
b < 1
-4 |3 - 9n| < 5
no solution
Isolate x:
z = mx + yx
x = z/(m+y)
Before a piece of steel can be sold for it's max price, it must be 35 feet long with an absolute deviation of 1.5 feet. Find the range of acceptable heights for steel that are to be sold at full price by writing an absolute value inequality to represent the situation.
33.5 ft <= x <= 36.5 ft