After completing this chapter, students will be able to: Explain the basic procedures used to solve equations for the unknown; list the five rules and the mechanical steps used to solve for the unknown in seven situations; know how to check the answers; list the steps for solving word problems; complete blueprint aids to solve word problems; check the solutions. | Chapter Five Solving for the Unknown: A How-To Approach for Solving Equations Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin LU 5-1: Solving Equations for the Unknown Explain the basic procedures used to solve equations for the unknown. List the five rules and the mechanical steps used to solve for the unknown in seven situations; know how to check the answers. LU 5-2: Solving Word Problems for the Unknown List the steps for solving word problems. Complete blueprint aids to solve word problems; check the solutions. Learning unit objectives Terminology Expression – A meaningful combination of numbers and letters called terms. Equation – A mathematical statement with an equal sign showing that a mathematical expression on the left equals the mathematical expression on the right. Formula – An equation that expresses in symbols a general fact, rule, or principle. Variables and constants are terms of mathematical expressions. Solving Equations . | Chapter Five Solving for the Unknown: A How-To Approach for Solving Equations Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin LU 5-1: Solving Equations for the Unknown Explain the basic procedures used to solve equations for the unknown. List the five rules and the mechanical steps used to solve for the unknown in seven situations; know how to check the answers. LU 5-2: Solving Word Problems for the Unknown List the steps for solving word problems. Complete blueprint aids to solve word problems; check the solutions. Learning unit objectives Terminology Expression – A meaningful combination of numbers and letters called terms. Equation – A mathematical statement with an equal sign showing that a mathematical expression on the left equals the mathematical expression on the right. Formula – An equation that expresses in symbols a general fact, rule, or principle. Variables and constants are terms of mathematical expressions. Solving Equations for the Unknown Left side of equation Right side of equation Equality in equations A + 8 58 Dick’s age in 8 years will equal 58. 4 Variables and Constants Rules If no number is in front of a letter, it is a 1: B = 1B; C = 1C If no sign is in front of a letter or number, it is a +: C = +C; 4 = +4 5 Solving for the Unknown Rule Whatever you do to one side of an equation, you must do to the other side. 6 Opposite Process Rule If an equation indicates a process such as addition, subtraction, multiplication, or division, solve for the unknown or variable by using the opposite process. 7 Opposite Process Rule A + 8 = 58 - 8 - 8 A = 50 Check 50 + 8 = 58 8 is subtracted from both sides of equation to isolate variable A on the left. 8 Equation Equality Rule You can add the same quantity or number to both sides of the equation and subtract the same quantity or number from both sides of the equation without affecting the equality of the equation. You can also divide or multiply both sides of the .
