Transcript 1.3 Objective: Solving Linear Equations

Equation:
A statement that two
expressions are =
Linear
Equation: Can be written
in the form ax + b = 0 (a and b
are coefficients and a≠0)
 Addition
Property of Equality
 Subtraction Property of Equality
 Multiplication Property of Equality
 Division Property of Equality
Your
goal when solving for a
variable is to isolate that
variable on one side.
To
move something to the
other side of the = sign,
simply use the opposite
operation.

x + 8 = 11

y–4=7

5d = 30

½x = 25

1 = 1/3a – 5

3 = 2p + 5

7 – 5/3c = 22

5w + 2 = 2w + 5

p + 5 = 25 – 4p
17
– 6r = 25 – 3r

2(b + 3) = 4b – 2
10(w
– 4) = 4(w + 4) + 4w
Look
at problems 63 and 65
Solution:
A number is a solution of
an equation if substituting the
variable results in a true statement
 Example: n + 3 = 5, 2 is a solution
because substituting 2 gives a true
statement
(2) + 3 = 5
5=5
Equivalent
solutions
equations have the same
You
are a waiter/waitress at a
restaurant. You earn $30 for your
shift, but you also get an additional
15% in tips on customers’ food bills.
You leave with $105 for the day.
What was the total of the
customers’ food bills?
The
bill for the repair of your
bicycle was $180. The cost of parts
was $105. The cost of labor was $25
per hour. How many hours did the
repair work take?
Example 5 (in your book)
It
takes you 8 minutes to wash a
car and it takes a friend 6
minutes to wash a car. How long
does it take the two of you to
wash 7 cars if you work
together?
Extra Example 5 (not in book)
It
takes you 45 mins to mow your
lawn and it takes your brother 30
mins to mow the lawn. How long
does it take you to mow the lawn if
you have two mowers and work
together?
 What
are you allowed to do to an
equation?
 When
solving for a variable, what is your
goal?
 You
should never get the answers wrong
when solving for linear equations. Why?
12-46
even, 68, 70, 71, 73, 75 –
77
 Bonus:
67, 78