4 Solving Equations 4.1 Simplifying Expressions and Combining Like Terms 4.2 Addition and Subtraction Properties of Equality 4.3 Multiplication and Division.

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Presentation transcript:

4 Solving Equations 4.1 Simplifying Expressions and Combining Like Terms 4.2 Addition and Subtraction Properties of Equality 4.3 Multiplication and Division Properties of Equality 4.4 Solving Equations with Multiple Steps

4.1 Homework Questions?

Addition and Subtraction Properties of Equality 4.2 Addition and Subtraction Properties of Equality 1. Definition of a Linear Equation in One Variable 2. Addition and Subtraction Properties of Equality

Addition and Subtraction Properties of Equality 4.2 Addition and Subtraction Properties of Equality 1. Definition of a Linear Equation in One Variable An equation is a statement that indicates that two quantities are equal. A solution to an equation is a value of the variable that makes the equation a true statement.

Addition and Subtraction Properties of Equality 4.2 Addition and Subtraction Properties of Equality 1. Definition of a Linear Equation in One Variable Note: A linear equation in one variable contains only one variable and the exponent on the variable is 1.

Linear Equation in One Variable Let a and b be numbers such that a 0. A linear equation in one variable is an equation that can be written in the form ax + b = 0

It is important to distinguish between an equation and an expression It is important to distinguish between an equation and an expression. An equation has an equal sign, whereas an expression does not. For example: 2x + 4 = 16 equation 7x – 9 expression

Determining Whether a Number Is a Solution to an Equation 1 Determining Whether a Number Is a Solution to an Equation Determine whether the given number is a solution to the equation. .

4.2 You Try Determine if the provided value is a solution for the given equation. 6 – 3x = 7 (-1) 7x + 4 = 3x + 2 (5)

Addition and Subtraction Properties of Equality 4.2 Addition and Subtraction Properties of Equality 2. Addition and Subtraction Properties of Equality Two equations are called equivalent equations if they have the same solution.

Addition and Subtraction Properties of Equality

4.2 To solve an equation, the goal is to isolate the variable on one side of the equation. That is, we want to create an equivalent equation of the form variable = constant. To accomplish this, we can use the fact that the sum of a number and its opposite is zero.

2 Applying the Addition Property of Equality

3 Applying the Subtraction Property of Equality

4.2 You Try Solve and check. a – 9 = -14 x – 5 = 7 x + 6 = 4

Solving Equations Using the Distributive Property Use the distributive property to remove any grouping symbols. Combine like terms on each side of the equation. Use the Addition or Subtraction Property of Equality to solve the equation. Check your solution.

Applying the Addition and Subtraction Properties of Equality 4 Applying the Addition and Subtraction Properties of Equality .

4.2 You Try Solve. Remember that you should simplify the expressions on each side of the equation before using the equality property to solve. x + 3 – 5 = 8 + 2 4(x + 2) - 3x = 17

Addition and Subtraction Properties of Equality 4.2 Addition and Subtraction Properties of Equality 1. Definition of a Linear Equation in One Variable 2. Addition and Subtraction Properties of Equality