8 Chapter Chapter 2 Introduction to Algebra

Solving Equations: Using the Addition and Multiplication Properties Section 8.4 Solving Equations: Using the Addition and Multiplication Properties

Solve Equations Using Addition and Multiplication Properties. Objective A Solve Equations Using Addition and Multiplication Properties.

Steps for Solving an Equation Step 1: If parentheses are present, use the distributive property. Step 2: Combine any like terms on each side of the equation. Step 3: Use the addition property of equality to rewrite the equation so that variable terms are on one side of the equation and constant terms are on the other side. Step 4: Use the multiplication property of equality to divide both sides by the numerical coefficient of the variable to solve for. Step 5: Check the solution in the original equation. Objective A

Example Solve 3x – 12 = 24 Check: Objective A

Example Solve: 17 – x + 3 = 15 – (–6) Objective A

Example Solve: Objective A

Example Solve: 7x + 3.2 = 4x – 1.6 Objective A

Solve Equations Containing Parenthesis. Objective B Solve Equations Containing Parenthesis.

Example Solve: 7(x – 3) = 9x – 8 Objective A

Write Numerical Sentences as Equations. Objective C Write Numerical Sentences as Equations.

Writing Sentences as Equations Key Words or Phrases Examples Symbols equals 3 equals 2 plus 1 3 = 2 + 1 gives the quotient of 10 and –5 gives –2 is/was 17 minus 12 is 5 17 – 12 = 5 yields 11 plus 2 yields 13 11 + 2 = 13 amounts to twice –15 amounts to –30 2(–15) = –30 is equal to –24 is equal to 2 times –12 –24 = 2(–12) Objective A

Example Translate each sentence into an equation. a. The product of 7 and 6 is 42. 7(6) = 42 b. Twice the sum of 3 and 5 is equal to 16. 2(3 + 5) = 16 Objective A