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Algebra 1 – 3.3 – Solving Multi-Step Equations
Application Lesson Opener
1)
2)
3)
An electrician charges $15 per service call plus $25 an hour plus the cost of the parts
used. The total bill for a recent job was $155. If the parts for this job cost $65 and x
represents the number of hours worked, which equation can be used to model this
problem?
a)
15 + 25 + x + 65 = 155
b)
15x + 25 + 65 = 155
c)
15 + 25x + 65 = 155
d)
15 + 25 + 65x = 155
On a recent trip to a computer store, you purchased one software package for
$24.99 and three printer cartridges. The total bill with tax was $90.91. If the tax was
$5.95 and x represents the cost of each printer cartridge, which equation can be
used to model this problem?
a)
24.99 + 3x + 5.95 = 90.91
b)
24.99 + 3 + x + 5.95 = 90.91
c)
24.99 + 3x(5.95) = 90.91
d)
5.95(24.99 + 3x) = 90.91
You subscribed to a long-distance calling plan that costs $12.99 a month plus $0.09
per minute for all long-distance calls. Your total long-distance bill last month was
$21.54. If x represents the number of long-distance minutes you used last month,
which equation can be used to model this problem?
a)
12.99 + 0.09 + x = 21.54
b)
21.54 – 0.09 – x = 12.99
c)
12.99x + 0.09 = 21.54
d)
0.09x + 12.99 = 21.54
Steps for Solving Multi-Step Equations
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2)
3)
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5)
6)
1
Algebra 1 – 3.3 – Solving Multi-Step Equations
Examples:
Solve the following equations.
a)
1
x + 6 = -8
3
b)
c)
7x – 3x – 8 = 24
d)
5 = 3x – 7 + x
e)
5x + 3(x + 4) = 28
f)
17 = 2(3x +1) – x
g)
4x – 3(x – 2) = 21
h)
106 = 6x – 4(9 – x)
i)
4
- (2x – 4) = 48
9
j)
6
66 = - (x + 3)
5
30 = 16 +
1
x
5
2
Algebra 1 – 3.3 – Solving Multi-Step Equations
Examples:
Solve the following real-life problems
a)
Checking Vital Signs: A body
temperature of 95F or lower may
indicate the medical condition called
hypothermia. What temperature in
the Celsius scale may indicate
hypothermia? The Fahrenheit and
Celsius scales are related by the
9
equation: F = C + 32.
5
b)
Science Connection: The
temperature within the Earth’s crust
increases about 30 Celsius for each
kilometer of depth beneath the
surface. If the temperature at Earth’s
surface is 24C, at what depth would
you expect the temperature to be
114C?
c)
Consecutive Integers: Find three
consecutive integers who sum is 84.
d)
Find the numbers: The sum of three
numbers is 123. The second number is
9 less than two times the first number.
The third number is 6 more than three
times the first number. Find the three
numbers.
3
Algebra 1 – 3.3 – Solving Multi-Step Equations
Graphing Calculator Activity: Use can use the “solve” feature of a graphing calculator to
solve equations. Kayla was here!!!
a)
3
x–6=9
4
b)
6x – 3x – 10 = 11
Set the equation = 0 (subtract 9 from both
sides)
Set the equation = 0 (subtract 11 from both
sides)
MATH, 0
(may then need to , CLEAR)
Type equation (3/4)x69
ENTER
ALPHA
ENTER
X = _____
MATH, 0
(may then need to , CLEAR)
Type equation 6x3x1011
ENTER
ALPHA
ENTER
X = _____
c)
8x – 2(x + 3) = 12
d)
3x – 5 = 13
e)
5
x + 7 = -8
4
f)
2x + 7 + 8 = 35
g)
11x + 3(x – 2) = -34
h)
27 = 9(3 – 2x)
i)
2
(x + 6) = -12
3
j)
k)
5x + 4 – 8x = 13
l)
x – (3x – 9) = -5
m)
13x – 4(2x – 5) = 15
n)
4x – (2x + 3) = 7
-8 =
1
x+x
3
4