1. Lesson 1 – 4
Solving Equations

2. Objectives
Translate verbal expressions into algebraic expressions, and vice versa.
Solve equations using the properties of equality.

3. Verbal & Algebraic Expressions
Verbal expressions can be translated into algebraic or mathematical expressions using the language of algebra.
Any letter can be used as a variable to represent a number that is not known.

4. Example 1
Write an algebraic expression to represent each verbal expression.
7 less than a number
Three times the square of a number
The cube of a number increased by 4 times the same number
Twice the sum of a number and 5
x – 7
3x2
n3 + 4n
2(a + 5)

5. Mathematical Sentences
A mathematical sentence containing one or more variables is called an open sentence.
A mathematical sentence stating that two mathematical expression are equal is called an equation.

6. Example 2 Write a verbal sentence to represent each situation.
10 = 12 – 2
n + (-8) = -9
Ten is equal to twelve minus two.
The sum of a number and -8 is equal to -9.
The quotient of a number and 6 is equal to that number squared.

7. Replacements & Solutions
Open sentences are neither true nor false until the variables have been replaced by numbers.
Each replacement that results in a true sentence is called a solution of the open sentence.

8. Properties of Equality
Property
Symbols
Reflexive
For any real number a, a = a.
Symmetric
For all real numbers a and b, if a = b, then b = a.
Transitive
For all real numbers a, b, and c, if a = b and b = c, then a = c.
Substitution
If a = b, then a may be replaced by b in any expression.

9. Example 3 Name the property illustrated.
If 3m = 5n and 5n = 10p, then m = 10p.
If -11a + 2 = -3a, then -3a = -11a + 2.
Transitive Property
Symmetric Property

10. Addition & Subtraction Properties
For any real numbers a, b, and c, if a = b, then

11. Multiplication & Division Properties
For any real numbers a, b, and c, if a = b, then

12. Example 4 Solve the following equation. Check your answer.
Subtract 4.39 from each side.

13. Calculator Check

14. Example 5
Multiply both sides by the reciprocal.

15. Calculator Check

16. Example 6 Complete each distribution. Combine like terms.
Subtract 21 from each side.
Divide each side by -8.

17. Example 7 Solve the formula for l. Subtract from each side.
Divide each side by

18. SOL Problem