Transcript Lesson 1.3

Lesson 1.3
Essential Question: How do I solve an equation with
variables on both sides of an equal sign.
Objective: To solve equations with variables on
both sides of the equal sign
Example:
12 + 4x = 10x
– 4x – 4x
12 = 6x
6
6
2=x
Subtract 4x from both sides.
Divide both sides by 6.
Solution
Check: 12 + 4(2) = 10(2)
20 = 20
Example:
50 + 9x = 4x
– 9x – 9x
Subtract 9x from both sides.
50 = – 5x
–5
–5
Divide both sides by – 5.
– 10 = x
Solution
Check:
50 + 9(-10) = 4(-10)
50 + (-90) = -40
– 40 = – 40
Example:
1
10 x  20  3  2 x
2
5x – 10 = 3 + 2x
– 2x
– 2x
3x – 10 = 3
+10 +10
3x
3
= 13
3
1
13
x=
or 4
3
3
1
Distribute the
2
Subtract 2x from both sides.
Add 10 to both sides
Divide both sides by 3
Sometimes an equation does not have only one
solution. Some equations have many solutions while
others have no solutions.
Identity: Is an equation that is true for all values of
the variable. (All real numbers are true)
Example:
4(x + 2) = 8 + 4x
4x + 8 = 8 + 4x
– 4x
– 4x
8=8
All real numbers
Distribute the 4
Subtract 4x from both sides
True, Therefore this is an identity
and all real numbers are solutions
To check, Replace x with any number
Example:
9x + 4 = 7 + 9x
– 9x
– 9x
4=7
4=7
No Solution
Subtract 9x from both sides
False 4 does not equal 7
therefore there are no
solutions. There is no number
that will make this true.
Verbal Models/Problem Solving
Example:
Hank’s video store charges $8.00 to rent a video game
for five days and does not charge an annual membership
fee. Bunker’s video only charges $3.00 for a five day
rental but has a $50.00 membership fee per year.
Find the number of rentals that would cost the same from each store.
Hanks
Number
Rented
Charges
8
•
x
=
Bunkers
Charges
=
3
Number
Rented
•
x
Membership
+ Fee
+
50
Subtract 3x from both sides
8x = 3x + 50
5x = 50
Divide both sides by 5
X = 10
If you rent 10 games per year, the
cost would be the same.
Review your left column questions.
Suggestion: How do you tell the difference between an
equation with no solutions and many solutions?
Write a summary