 # Section 2.1 Solving Equations Using Properties of Equality.

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Section 2.1 Solving Equations Using Properties of Equality

Objectives Determine whether a number is a solution Use the addition property of equality Use the subtraction property of equality Use the multiplication property of equality Use the division property of equality

Objective 1: Determine Whether a Number is a Solution An equation is a statement indicating that two expressions are equal, for example:  x + 5 = 15  x + 5 is the left side  15 is the right side A number that makes an equation true when substituted for the variable is called a solution and it is said to satisfy the equation. The solution set of an equation is the set of all numbers that make the equation true.

EXAMPLE 1 Check to determine whether 9 is a solution of 3y – 1 = 2y + 7?

Objective 2: Use the Addition Property of Equality To solve an equation means to find all values of the variable that make the equation true. Equations with the same solutions are called equivalent expressions. Addition property of equality: Adding the same number to both sides of an equation does not change its solution.  For any real numbers a, b, and c, if a = b, then a + c = b + c

EXAMPLE 2 Solve: x – 2 = 3

Objective 3: Use the Subtraction Property of Equality Since any subtraction can be written as an addition by adding the opposite of the number to be subtracted, this property is an extension of the addition property of equality. Subtraction property of equality: Subtracting the same number from both sides of an equation does not change its solution.  For any real numbers a, b, and c, if a = b, then a – c = b – c

EXAMPLE 4 Solve: a. x + 1/8 = 7/4 b. 54.9 + x = 45.2

Objective 4: Use the Multiplication Property of Equality Multiplication property of equality: Multiplying both sides of an equation by the same nonzero number does not change its solution.  For any real numbers a, b, and c, where c is not 0, if a = b, then ca = cb

EXAMPLE 5

Objective 5: Use the Division Property of Equality Division property of equality: Dividing both sides of an equation by the same nonzero number does not change its solution.  For any real numbers a, b, and c, where c is not 0, if a = b, then a/c = b/c

EXAMPLE 7 Solve: a.2t = 80 b. –6.02 = –8.6t