1. Equations and their Solutions#7

2. VOCABULARY
An equation is a mathematical statement that two expressions are equal. You can think of a correct equation as a balanced scale.
3 + 2 5

3. s = 12 is a solution because 12 + 15 = 27.
VOCABULARY
Equations may contain variables. If a value for a variable makes an equation true, that value is a solution of the equation.
s + 15 = 27
s = 12
s = 10 27 27
s = 12 is a solution because = 27.
s = 10 is not a solution because  27.

4. The symbol  means “is not equal to.”
Reading Math

5. Example 1: Determining Solutions of Equations
Determine whether the given value of the variable is a solution.
b — 447 = 1,203 for b = 1,650

6. Example 2: Determining Solutions of Equations
Determine whether the given value of the variable is a solution.
27x = 1,485 for x = 54

7. Example 3
Determine whether the given value of the variable is a solution.
A. u + 56 = 139 for u = 73

8. Example 4
Determine whether the given value of the variable is a solution.
B. 45 = v for v = 55

9. Example 5 C. 26x = 13 for x = 2 26 × 2 = 52, not 13;
Determine whether the given value of the variable is a solution.
C. 26x = 13 for x = 2
26 × 2 = 52, not 13;
2 is not a solution.

10. An equation has an equal sign, but an expression does not
An equation has an equal sign, but an expression does not. An equation can be solved, but an expression can only be evaluated or simplified.
Reading Math

11. Real-World Application: Example 6
Determine whether the given value of the variable is a solution.
Anna says that the table is 7 feet long. John says that the table is 84 inches long . Determine if these two measurements are equal.

12. Real-World Application: Example 7
Determine whether the given value of the variable is a solution.
Ten Museum Park is a skyscraper in Miami, Florida. It is 585 feet tall. Jerry says that its height is 195 yards. Is Jerry correct?

13. Real-World Application: Example 8
Determine whether the given value of the variable is a solution.
Ralph pays $2 for an individual slice of Pizza. He can buy the entire 8-slice pizza for $12. Is this what he would pay for 8 individual slices?