### Solving Multi-Step Equations

```Solving Multi-Step Equations
An alligator hatchling 6 inches long grows about 12 inches per year. The expression 12a + 6 represents the
length in inches of an alligator that is "a" years old.
·What does the number 6 represent in the expression 12a + 6?
·What does the 12a represent in the expression 12a + 6?
·What does this expression assume about the growth of an alligator over its
·How old is the alligator if it is 11 feet 6 inches long?
7m - 17 = 60
21 = 14
2a - 6 = 4
8 = 3r + 7
t/8 +
Two-Step
Algebra
Subject:
Date:
1
5q - 13 = 27
2
4g - 2 = -6
3
18 = 5p + 3
4
9 = 1 + m/7
5
(3/2)a - 8 = 11
·(p - 15)/9 = - 6
p = -39
·(k - 12)/5 = 4
k = 32
·(n + 1)/ -2 = 15
n = - 31
binomial-Proportion
Algebra
Subject:
Date:
1
20 = (n - 3)/8
2
(b + 4)/ -2 = - 17
Allen is buying a pair of water skis that are on sale for 2/3 of the original price. After he uses a \$25 gift
certificate, the total cost before taxes is \$115. What was the original price of the skis? Write an equation
for the problem and solve.
(2/3)p - 25 = 115
p = \$210
Susan had a \$10 coupon for the purchase of any item. She bought a coat that was on sale for
½ its original price. After using the coupon, Susan paid \$125 for the coat before taxes. What
was the original price of the coat? Write and solve and equation.
(½)p - 10 = 125
p = \$270
Alex belongs to the Student Music Club and bought a discount card for \$19.95. After one
year, Alex has spent \$63.40. Each CD cost \$3.95. Write and solve an equation to find ho
many CDs Alex bought during the year.
Total Cost = Cost of CDs + Cost of Discount Card
63.40 = 3.95C + 19.95
Solve.
11 = C, or Alex bought 11 CDs during the year.
Sara paid \$15.95 to become a member at a gym. She then paid a monthly membership fee
Her total cost for 12 months was \$735.95. How much was the monthly fee?
Total Cost = Monthly Fee + Membership Fee
735.95 = 12 F
+ 15.95
Solve.
F = 60, or Sara paid \$60 each month.
Lynda has 12 records in her collection. She adds the same number of new records to he
collection each month. After 7 months Lynda has 26 records. How many records does
Total Number = Number Added each month + Original Number
26 = 7R + 12
Solve.
R = 2, or Lynda adds 2 new records each month.
Jan joined the dining club at the local cafe for a fee of \$29.95. Being a member
entitles her to save \$2.50 every time she buys lunch. Jan calculates that she has
saved a total of \$12.55 so far by joining the club. Writes and solve an equation to find
how many times Jan has eaten lunch at the cafe.
Total Savings = Savings each time - Original Fee
12.55 = 2.50x - 29.95
Solve.
x = 17, or Jan has eaten lunch 17 times at the cafe.
Application
Algebra
Subject:
Date:
1
Twelve decreased by twice a number equals - 34. Write and solve an
equation.
A
23
B
35
C
92
D
17.5
2
The English alphabet contains 2 more than twice as many letters as the
Hawaiian alphabet. How many letters are there in the Hawaiian alphabet?
Simplify Before Solving
Justify each step
6x + 3 - 8x = 13
6x - 8x + 3 = 13 Commutative
(6x - 8x) + 3 = 13 Associative
x(6-8) + 3 = 13
Distributive
-2x + 3 = 13
-3
-3
Sub. Prop of
Equality
-2x = 10
/-2
/-2
Div. Prop of
Equality
x = -5
Simplify Before Solving
Justify each step
2a + 3 - 8a = 8
a = (-5/6)
Simplify Before Solving
Justify each step
-8 - 2d + 2 = 4
d = -5
Simplify Before Solving
Justify each step
4x - 8 + 2x = 40
x=8
Simplify Before Solving
Justify each step
8x - 21 - 5x = -15
x=2
Simplify Before Solving
Justify each step
4 = 2x + 5 - 6x
x = (1/4)
Write and Solve an equation for the following problem.
Find three consecutive even integers whose sum is -42.
Let n = the least even integer
Then n + 2 = the next greater even integer and n + 4 = the greatest of the three even integers.
n + (n + 2) + (n + 4) = - 42
n = -16
-16, -14, -12
Consecutive Integers
Algebra
Subject:
Date:
1
Find three consecutive integers with a sum of 42
A
12,13,14
B
13,14,15
C
14,15,16
2
Find three consecutive even integers with a sum of -12
A
-2, 0, 2
B
-4, -2, 0
C
-6, -4, -2
3
What is the greatest integer for the following:
Find three consecutive odd integers whose sum is 57.
Math Is Everywhere!.mp3
Simplifying Using the Distributive Property
9 = 6 - (x + 2)
9 = 6 + (-1)x + (-1)2
9 = 6 + -1x + -2
9 = (6-2) + -1x
9=4-x
5 = -x
-5 = x
Simplifying Using the Distributive Property
4(x + 1) + 2( x - 7) = 50
4x + 4(1) + 2x + 2(-7) = 50
4x + 4 + 2x + -14 = 50
(4x + 2x) + (4 - 14) = 50
6x - 10 = 50
x = 10
Simplifying Using the Distributive Property
5(p - 2) = -15
p = -1
Simplifying Using the Distributive Property
10y - (4y + 8) = -20
y = -2
Distributive Property
Algebra
Subject:
Date:
1
5(2y - 7) + 8(y + 6) = 31
2
4x - 3(6 + x) - 1 = 2
3
17 - (4 - 6z) + 4 = 42
4
42r - 2(13 - 5r) + 7 = 85
5
3(x - 2) - 5(2x + 1) = 3
Attachments
Math Is Everywhere!.mp3
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