Solving Equations
- 1. Equations in One Variable • Lesson 4.1 – Page 89-96 Copyright © 2012, 2008, 2004 Pearson Education, Inc.
- 2. Equations and inequalities compare algebraic expressions. An equation is a statement that two algebraic expressions are equal. An equation always contains an equals symbol, while an expression does not. 3x – 7 = 2 3x – 7 Left side Right side Equation (to solve) Copyright © 2012, 2008, 2004 Pearson Education, Inc. Expression (to simplify or evaluate) Slide 2.1- 2 Distinguish between expressions and equations.
- 3. Decide whether each of the following is an equation or an expression. 9x + 10 = 0 9x + 10 equation expression Copyright © 2012, 2008, 2004 Pearson Education, Inc. Slide 2.1- 3 CLASSROOM EXAMPLE 1 Distinguishing between Expressions and Equations Solution:
- 4. Linear Equation in One Variable A linear equation in one variable can be written in the form Copyright © 2012, 2008, 2004 Pearson Education, Inc. Ax + B = C, where A, B, and C are real numbers, with A ¹ 0. A linear equation is a first-degree equation, since the greatest power on the variable is 1. Slide 2.1- 4 Identify linear equations, and decide whether a number is a solution of a linear equation.
- 5. More Properties of Equality If the operation done to one side is also done to the other then the value of the equation does not change PAGE 89 Definition Examples • Addition: If a=b, then a + c = b + c • Subtraction: If a=b, then a – c = b – c Multiplication: If a=b, then a ∙ c = b ∙ c • Division: If a = b, then a / c = b / c (c≠0) Copyright © 2012, 2008, 2004 Pearson Education, Inc. • If x = 12, then x + 3 = 12 + 3 • If x = 12, then x – 3 = 12 – 3 • If x = 12, then x ∙ 3 = 12 ∙ 3 • If x = 12, then x / 3 = 12 / 3
- 6. CLASSROOM EXAMPLE 2 Using the Properties of Equality to Solve a Linear Equation Solve. 4x + 8x = –9 + 17x – 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc.
- 7. Solving a Linear Equation in One Variable Step 1 Clear fractions or decimals. Eliminate fractions by multiplying each side by the least common denominator. Eliminate decimals by multiplying by a power of 10. Step 2 Simplify each side separately. Use the distributive property to clear parentheses and combine like terms as needed. Step 3 Isolate the variable terms on one side. Use the addition property to get all terms with variables on one side of the equation and all numbers on the other. Step 4 Isolate the variable. Use the multiplication property to get an equation with just the variable (with coefficient 1) on one side. Step 5 Check. Substitute the proposed solution into the original equation. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Slide 2.1- 7 Solve linear equations by using the addition and multiplication properties of equality.
- 8. Type of Linear Equation Number of Solutions Copyright © 2012, 2008, 2004 Pearson Education, Inc. Indication when Solving Conditional One Final line is x = a number. Identity Infinite; solution set {all real numbers} Final line is true, such as 0 = 0. Contradiction None; solution set Æ Final line is false, such as –15 = –20 . Slide 2.1- 8 Identify conditional equations, contradictions, and identities.