Lesson 1 – 4 Solving Equations.

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Presentation transcript:

Lesson 1 – 4 Solving Equations

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

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.

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)

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.

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.

Replacements & Solutions Open sentences are neither true nor false until the variables have been replaced by numbers.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.

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.

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

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

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

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

Calculator Check

Example 5 Multiply both sides by the reciprocal.

Calculator Check

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

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

SOL Problem