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Chapter 3 – Solving Linear Equations
Algebra I A - Meeting 12
Section 3.1 – Solve One-Step Equations
Inverse Operations – are two operations that undo each other, such as addition and
subtraction.
Equivalent Equations – are equations that have the same solution(s).
Example # 1
Solve for x a) x  9  3
a) x  9  3
 9  9
b) x  2  11
Write the original equation.
c) 4 x  28
c) 4 x  28
 4 x   28
Subtract 9 from each side
 4  4
Simplify
69 3
Check your Solution.
b) x  2  11
 2  2
Write the original equation.
Add 2 to each side of equation.
Simplify
13  2  11
11  11
Check your Solution.
Divide each side by - 4
Simplify
 4(7)  28
33
Write the original eq.
 28  28
Check your Solution.
Chapter 3 – Solving Linear Equations
Algebra I A - Meeting 12
Section 3.1 – Solve One-Step Equations
Example # 2
Solve for x
a)
x
7
3
x
7
3
3

x9
b)
a)
5
Write the original equation.
3

x  9 Write the original eq.
b)
5
Multiply each side by 3
 5  3   5
      x       (9)
3  5   3

Simplify
Multiply each side by the reciprocal, (-5/3)
21
7
3
77
Check your Solution.
Simplify
Simplify
3
 (15)  9
5
99
Work on pg 138 # 32 - 40 even
Check your Solution.
Chapter 3 – Solving Linear Equations
Algebra I A - Meeting 12
Section 3.2 – Solve Two-Step Equations
Example # 3
Solve for x
a)
x
3 2
4
x
3 2
a)
4
Write the original equation.
Isolate the Variable, by
adding 3 to each side.
x
Simplify
5
4
x
4   4  5 Multiply each side by 4
4
Simplify
20
3 2
4
53 2
22
b)
5x  7 x  4
b) 5x  7 x  4 Write the original eq.
 2x  4
Combine Like Terms,
by adding the x-variables coefficients
Divide each side by - 2
Simplify
5( 2)  7( 2)  4
 10  ( 14)  4
Check your Solution.
 10  14  4
44
Check your Solution.
Chapter 3 – Solving Linear Equations
Algebra I A - Meeting 12
Section 3.2 – Solve Two-Step Equations
Example # 4
The output of a function is 7 more than 2 times the input.
Find the input when the output is 15.
Write and equation for the equation for the function.
Let x be the input and y be the output.
y  2x  7
a) y  2 x  7 Write the equation for the function.
Substitute 15 for y.
15  2x  7 Isolate the Variable,
 7 Subtract 7 from each side.
7
8  2x
Simplify
Divide each side by 2.
Simplify
The input of the function (x-variable) is 4.
Check your Solution.
15  2(4)  7
15  8  7
15  15
Chapter 3 – Solving Linear Equations
Algebra I A - Meeting 12
Section 3.2 – Solve Two-Step Equations
Example # 5
To Rent a booth at the county fair-grounds cost $42 per day plus a
one-time equipment fee of $85. Find the number of days Mr. Woodson
rented a booth if he paid a total of $337.
Write a verbal model.
Total Price Paid
One-time
By Mr. Woodson = Equipment Fee +
(dollars)
(dollars)
Daily
Booth Cost *
(dollars per day)
Number of Days
Rented by Mr. Woodson
(days)
Write an Equation.
P
=
$ 85
+
P = $ 85 + $42 D
$337 = $ 85 + $42 D
$337 - $85 = $85 - $85 + $42 D
$252 = $42 D
$252/$42 = ($42 D)/$42
$42
*
D
Write Equation
Substitute $337 for P
Subtract $85 from each side
Simplified Equation
Divide $42 from each side
6 =D
Simplified Equation
Mr. Woodson rented a county fair-grounds booth for a total of 6 Days.
Chapter 3 – Solving Linear Equations
Section 3.1, 3.2
Homework # 9
pg 132 # 32 – 40 even (if you didn’t finish in class)
pg 144 - 145 # 3 – 36 mult. of 3; # 38, # 41
Algebra I A - Meeting 12