1. 1.8: Intro to Equations
Equation: A mathematical sentence that uses the equal ( = ) sign. Ex: 3x=12, -1(x + 5) = 8,
Open Sentence: An equation that contains one or more variables Ex: 3x+ 7 = 21, 2y -5 = y + 8

2. Solution: The value of the variable that makes the equation true.
Ex: x+5 = 20
 3x = 20-5
 x = 15/3
x = 5

3. GOAL:

4. Identifying solutions:
We must be able to show if a digit is a solution to an equation.
Ex: Decide if the given number is a solution: 5b + 1 = 16; -3
Solution: To show if b=3 is a solution, we must substitute:
5( -3 ) + 1 = 16
= 16
–14= 16
Since -14 is not equal to 16, b=-3 is not a solution to the equation.

5. Ex: is m = ½ a solution to 6m – 8 = -5?
Solution: To show if m= ½ is a solution, we must substitute:
6( ½ ) – 8 = –5
3– 8 = –5
– 5 = –5
Since -5 is equal to -5, m=½ is a solution to the equation.

6. REAL-WORLD:
The equation p = c gives the cost in dollars that a store charges to deliver an appliance that weights p pounds. Use the equation an a table to find the weight of an appliance that costs $55 to deliver.

7. SOLUTION: Using the given equation and the table we have:
P in lbs p c 50
(50)
$ 37.5
100
(100)
$50
110
(110)
$52.50
120
(120)
$55
Therefore an appliance that weights 120 lbs will cost $55 to deliver.

8. Solving Equations: To solve an equation we must ISOLATE the variable involved by using opposite math operations to the ones the equation has.
Ex: Find the solution to the equations:
a) 2x - 3 = 11 b) x + 4 = - 2

9. Solution: a) 2x – 3 = 11 b) x + 4 = – 2 + 3 + 3 – 4 = –4 2x = 14
– 4 = –4
2x = 14
x = –6
x = 14/2
x = 7
Don’t forget to CHECK to make sure you got the correct solution.

10. CHECK: Replace your answer in the original equation to make sure you got the correct solution.
Ex: a) 2x - 3 = b) x + 4 = – 2
2(7) – 3 = 11
(– 6 )+ 4 = – 2
14 – 3 = 11
– 2 = –2
11 = 11
Both integers, the left and the right, coincide thus we have gotten the correct solution.

11. VIDEOS: Intro to Equations Solving:

12. Class Work:
Pages: 56 – 58
Problems: As many as you need to master the concepts.