1. Warm Up 10/23/12 To become a member of an ice skating rink,
you have to pay a $30 membership fee. The cost of admission to the rink is $5 for members and $7 for nonmembers. After how many visits to the rink is the total cost for members, including the membership fee, the same as the total cost for nonmembers?
Write an equation and solve.

2. Solving Linear Equations (Flow Map)
Parenthesis
Distributive Property
Yes
Combine Like Terms
(each side separately) No
Solving Linear Equations (Flow Map)
Box Variables
Separate Sides
Variables on Both Sides?
Isolate Variable On One Side
(Additive Inverse)
Yes
Move Constant To Other Side
(Additive Inverse) No
Isolate Variable On One Side
(Multiplicative Inverse)
Box Your Answer
Check Your Answer!
© Eugene Ruben Ramirez

3. is an equation that is true for all values of the variable.
Topic: Solving Equations With Variables
on Both Sides
Essential Question: How do we solve
equations with Variables on both sides
Standard: 8.EE.7
Identity:
is an equation that is true for all values
of the variable.

4. Solve 1) 4x –10 = 32 – 3x 4x –10 = 32 – 3x +3x +3x 7x –10 = 32 +10 +10
Question /
Key Words
Notes or Solutions to Problems
Solve 1)
4x –10 = 32 – 3x 4x
–10 = 32
– 3x
+3x
+3x 7x
–10 = 32
+10
+10 1 7x = 42 x = 6

5. 5x – 2 = 3x + 6

6. 8y + 4 = 11y - 17

7. m – 1 = 9m + 15

8. Solve 2) 6x = 5x – 33 6x = 5x – 33 –5x – 5x x = -33 Question /
Key Words
Notes or Solutions to Problems
Solve 2)
6x = 5x – 33 6x = 5x
– 33
–5x
– 5x x =
-33

9. 8x = 6x - 14

10. Solve 3) 10x – 22 = -x 10x –22 = -x +x +x 11x –22 = +22 +22 11x = 22
Question /
Key Words
Notes or Solutions to Problems
Solve 3)
10x – 22 = -x
10x
–22 = -x +x +x
11x
–22 =
+22
+22 1
11x = 22 x = 2

11. 5x + 24 = -x

12. Solve 2x –9 + 7x = -34 – 3x +7x 9x – 9 = 4x – 34 –4x –4x 5x – 9 = – 34
Question /
Key Words
Notes or Solutions to Problems
Solve 4) 2x –9
+ 7x =
-34
– 3x
+7x
2x – 9 + 7x = -34 – 3x +7x 9x
– 9 = 4x
– 34
–4x
–4x 5x
– 9 =
– 34 +9 +9 1 5x =
-25 x = -5

13. 6y + 7y + 19 = y

14. is an equation that is true for all values of the variable.
Topic: Solving Equations With Variables
on Both Sides
Essential Question: How do we solve
equations with Variables on both sides
Standard: 4.0
Identity:
is an equation that is true for all values
of the variable.

15. Solve 9x – (x + 6) 1 = -2(x – 6) + 5 9x –1x –6 = -2x + 12 + 5 8x –6 =
Question /
Key Words
Notes or Solutions to Problems
Solve 9x
– (x + 6) 1 =
-2(x – 6)
+ 5 5)
9x – (x + 6) = -2(x – 6) +5 9x
–1x –6 =
-2x
+ 12
+ 5 8x –6 =
-2x
+ 17
+2x
+2x
10x
– 6 = 17 +6 +6 1
10x = 23 3 2 x = 10

16. 2(4x + 5) = 8x + 10 8x + 10 = 8x + 10 –8x –8x 10 = 10 Identity 6)
Question /
Key Words
Notes or Solutions to Problems
Solve the equation if
possible. Determine
whether it has one solution,
no solution, or is an identity.
2(4x + 5) = 8x
+ 10 8x
+ 10 = 8x
+ 10 6)
2(4x + 5) = 8x + 10
–8x
–8x 10 = 10
Answer: The equation 10 = 10 is always
true, so all values of x are solutions.
The original equation is an identity.
Identity

17. x – 1 = x + 7 –x –x -1 = 7 No solution. 7) x – 1 = x + 7 Question /
Key Words
Notes or Solutions to Problems
Solve the equation if
possible. Determine
whether it has one solution,
no solution, or is an identity. x
– 1 = x
+ 7 –x –x 7)
x – 1 = x + 7 -1 = 7
Answer: The equation -1 = 7 is never
true no matter what the value of x.
The original equation has no solution.
No solution.

19. Vocabulary of Math Operations
Addition (+)
Subtraction (–)
Multiplication(), •
Division (÷)
sum
difference of
product
quotient
plus
minus
times
divide
added to
subtracted from
multiply
into
more than
less than
twice
ratio
increased by
decreased by
total
less