Two Step Equations
4m - 5 = 11
m = 4
8(n + 2) = 24
n = 1
operations that undo one another
inverse operations
The sum of three consecutive integers is 78. What are the three integers?
25,26,27
5m + 7 = 12
m = 1
-3d + 10 = 43
d = -11
-3 = -3(2t - 1)
t = 1
a statement that values two expressions as equivalent
equation
What property was used on 14k + 2(3k + 5) - 5 = 10 to obtain 14k + 6k + 10 - 5 = 10?
Distributive Property with the number 2.
x - 3(x + 4)= 10
x = -11
5h - 13 = 12
h = 5
(2(r - 3))/4 - 8 = 50
r = 119
using the properties of equality and inverse operations to get the variable alone on one side of equation
Isolate
Olivia ate at the same restaurant four times. Each visit she ordered a salad and left a $1.50 tip. She spent a total of $54. Find the cost c of each salad.
4c + 4*1.5 = 54
c = $12 per salad
Which property of real numbers is the following statement?
a + (b + c) = (a + b) + c
Commutative Property
-8 = 3y - 2
y = -2
-5(x - 3) = -25
x = 8
a symbol or letter that represents one or more numbers
variable
Darren wins a coupon for $4 off the lunch special for each of 5 days. He pays $75 for his 5 lunch specials. Write and solve an equation to find the original price p for one lunch special.
75/5 = p - 4
p = $19
If a = b, then b can replace a in any expression.
Substitution Property of Equality
p/4 + 6 = 8
p = 8
x - 2(x + 10) = 12
x = -32
any value that makes an equation true
solution to an equation
Renaldo catches the bus at 4:00 PM to ride 3.2 miles from his house to the dentist's office. He arrives at 4:30 PM, for a one-hour appointment. Then he will ride a bus traveling at the same rate of speed for 4.8 miles to the soccer field. Will he be on time for his 6:30 PM soccer practice?
3.2 miles = 0.5 hours ∙ r, so the rate of speed for the bus is 6.4 mph, and 4.8 miles will take 45 minutes. He is on time,because 5:30 p.m. plus 45 minutes is 6:15 p.m.
Casey buys sandwiches and bags of chips. Each sandwich costs three times as much as a bag of chips. She brought 5 sandwiches for $6 each and spent $42. How many bags b did she buy?
5 ∙ 6 + 2b = 42
6 bags of chips