Transcript Document
Welcome to Survey of Mathematics Unit 3 – Algebraic Expressions and Equations To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge the pod. To maximize chat, minimize roster by clicking here Agenda • • • • • Miscellaneous Administrative stuff Basic rules for simplifying expressions Basic rules for solving equations Applications of equations Wrap up Simplifying Expressions •Using the Order of Operations 1. Simplify within Parentheses 2. Simplify Exponents 3. Multiplication and Division 4. Addition and Subtraction •PEMDAS: “Please Excuse My Dear Aunt Sally” http://www.montanamath.org/?p=auntsally/pemdas Simplifying Expressions •Example: •Evaluate 3(x – 5)2 + 3x – 7, x = 6 This means to substitute 6 for x anywhere x appears in the expression 3(6 – 5)2 + 3(6) – 7 Parentheses = 3(1)^2 + 3(6) – 7 Exponents = 3(1) + 3(6) – 7 Multiplication & Division = 3 + 18 – 7 Addition = 21 – 7 Subtraction = 14 Simplifying Expressions •Some words you must know in order to be “Algebraically Literate”: •Term: A part of an expression joined to another part by addition or subtraction 3x – 2y + 5 has three terms •Numerical Coefficient (or just coefficient) – the number part of a variable term. In the term 3x, 3 is the coefficient •Factor: A part of an expression joined to another part by multiplication: 3(x – 2) means 3 times the quantity (x – 2)… 3 and (x – 2) are both factors Simplifying Expressions •Example: Simplify the expression 3x + 2(x – 3) + 1 First, use the distributive property: = 3x + 2x – 6 + 1 Second, add like terms. For terms with variables, we add like terms by adding coefficients. •Note – like terms are terms that have exactly the same variables) •Note: Change subtraction into the addition of a negative: = 5x + -6 + 1 = 5x + -5 = 5x – 5 Solving Linear Equations •Basics: •Always start by simplifying both sides •If you add, subtract, multiply or divide one side of the equation, you must do the same thing to the other side! •Gather like terms to one side using addition and subtraction rules •Isolate x by using division or multiplication Solving Linear Equations •Here’s a simple example to begin with… 3x – 24 = 42 In this example, our goal is to “isolate” x To do so, “undo” subtraction by adding 24 to both sides: 3x – 24 + 24 = 42 + 24 3x = 66 Next, to isolate x completely, divide both sides by 3: 3x / 3 = 66 / 3 x = 22 •Now don’t forget to check! •Check: 3(22) – 24 = 42 66 – 24 = 42 42 = 42 Solving Linear Equations Solve 4(x – 3) + 3 = 2(x + 1) – 3 4x – 12 + 3 = 2x + 2 – 3 Simplify 4x – 9 = 2x – 1 Gather x terms 4x – 2x – 9 = 2x – 2x – 1 2x – 9 = - 1 Gather Constants 2x – 9 + 9 = -1 + 9 2x = 8 Divide by 2 2x / 2 = 8 / 2 x=4 “Isolate x” Wrap up • Our seminar can be found in the archives by entering the seminar during the week… go to “Open Seminar” and find the old seminars there. • You can also access the notes and plenty of examples by going to “Doc Sharing” • Our three main topics were: – Expressions – Equations • Have a great week everyone!