2 1.6 Introduction to Solving Equations Objectives: Write and solve a linearequation in one variable. Solve a literalequation for a specified variable.Standard: D Formulate equationsto model routine and non-routine problem.
3 An equation is a statement that two expressions are equal.A variable is a symbol that represents many different numbers in a set of numbers.Any value of a variable that makes an equation true is a solution of the equation.
4 I. Properties of Equality For real numbers a, b, c:Reflexive Property a = aSymmetric Property If a = b, then b = a.Transitive Property If a = b and b = c, then a = c.Addition Property If a = b, then a + c = b + c.Subtraction Property If a = b, then a – c = b – c.Multiplication Property If a = b, then ac = bc.Division Property If a = b, then a c = b c, c 0.
5 I. Properties of Equality Tell which Properties of Equality you would use to solve each equation.1). 52 = -2.7x – 3Addition Property of EqualityDivision Property of Equality2). x = x + 222Multiplication Property of EqualitySubtraction Property of Equality
6 II. Substitution Property If a = b, you may replace a with b.Ex 1. The relationship between the Celsius temperature, C, and the Fahrenheit temperature, F, is given by F = 9/5 C Find the Celsius temperature that is equivalent to 86 F.
7 II. Substitution Property Using the equation given in Example 1, findthe Celsius temperature that is equivalent to122 F.
8 Solve 3x – 8 = 5x – 20. Check your solution by using substitution. Check the solution by substitution:
9 Solve 7 – 6x = 2x –9. Check your solution by using substitution.
10 III. An equation may also be solved by graphing!! Type it in y =. Use trace to find the point.Ex 1. Solve 3.24x – 4.09 = -0.72x by graphing.Type into your graphing calculator:Left side of equation: Right side of equation:y1 = 3.24x – y2 = -0.72x
11 III. An equation may also be solved by graphing!! Type it in y =. Use trace to find the point.Ex 2. Solve 2.24x – 6.24 = 4.26x – 8.76 by graphing.Left side of equation: Right side of equation:y1 = 2.24x – y2 = 4.26x -8.76x = 1.25
12 IV. Solve Multi-Step Equations Simplify each side of the equationDistributeCombine Like TermsAdd/subtract the smallest variable term (if there are variables on both sides)Solve the resulting one or two step equation
14 V. Literal Equations Ex 1. ½ bh = A for b Ex 2. P = 2l + 2w for w An equation that contains two or more variables.Formulas are examples of literal equations.Ex 1. ½ bh = A for bEx 2. P = 2l + 2w for w
15 V. Literal EquationsEx 3. A = ½ h(b1 + b2) for b2
16 Writing Activities: Solving Equations 9). Solve 5x – 1 = 3x – 15. Explain eachstep, and include the Properties ofEquality that you used.10). Explain how you can verify that3(2x + 5) = 9 + 3x and x = -2 areequivalent equations.