1. Equations and Their Solutions

2. Solutions of Equations
Definitions:
Equation – Is a mathematical statement that states that two expressions and or/quantities are equal.
Examples: = 10 3x = = x - 4
Solution of an Equation – Is the value or values that make an equation true.
Example: In the equation x + 4 = 7, “3” is the solution because it makes the equation true.

3. Solutions of Equations
Determining Whether the Given Values Are Solutions to the Equations
Example 1
a + 23 = 45 when a = 22
Example 2
60 ÷ c = 6 when c = 5
a + 23 = 45
= 45 ?
45 = 45
Original equation
60 ÷ c = 6
60 ÷ 5 = 6 ?
12 ≠ 6
Original equation
Substitute the value given for the variable.
Substitute the value given for the variable.
Determine whether the two sides of the equation are equal.
Determine whether the two sides of the equation are equal.
22 is a solution to this equation because 45 equals 45
5 is a not solution to this equation because 12 does not equal 6.

4. Solutions of Equations
Determine whether the given values are solutions to the equations.
1.) 3x = 33 when x = ) z – 14 = 23 when z = 36
3.) 34 = 17b when b = 2 4.) 56 ÷w = 7 when w = 4

5. Solutions of Equations
Real-Life Application
Rachel is setting up for a party. She has a total of 5 centerpieces but needs a total of 14. Write an equation to determine how many more centerpieces that she needs to buy?
If Rachel goes to the store to buy more centerpieces but they only have 7 available, will she have enough for the party?