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Module 6 Study Guide By: Ali Williams and Marietoni Manaloto 1. How to Translate a Verbal Expression into an Algebraic Expression Example: How To: Add Subtract Multiply Divide 1. First, you make a list of synonyms for each operation. Sum Difference Product Quotient Plus Minus Times Divided By More Than Less Than Of Groups Total Left In All 2. Then, you find the numerals and put them into the expression. 3. Be careful when translating Special Cases. The product of three and x, decreased by four. 3x-4 2. How to Use Distributive Property and Combining Like Terms to Simplify an Algebraic Expression How To: Example: 1. First, you make a table showing the terms that are alike. 2 2 7xy-4x y2 +2xy +6xy+3x y -7x2 y2 2. Then, you add or subtract to get the total, depending on the signs in front of the numbers. 3. Lastly, you create an expression. Starting with the largest exponent and going down to the plain number or lowest exponent. 2 2 7xy -4x y 6xy 3x 2y 2xy 2 -7x 2 y2 13xy -8x y 2 -8x2 y 2+2xy +13xy 2xy 2 2 2 3. How to Factor an Expression How To: Example: 1.First, you find the GCF (greatest common factor). 12x+21xy-18 2. Then, you use reverse distributive property to find the new, usable numbers. GCF= 3 3. Lastly, you multiply the GCF by the new numbers. This is your factored expression. 3(4x+7xy-6) 4. How to Write and Solve One-Step Addition and Subtraction Equations How To: Example: 1. First, to write an equation, you begin with the variable. X+3=2 2. Then, look at what numbers are negative vs. positive, and add or subtract them from x or add/subtract x from them. 3. To solve, you have to isolate the variable. To do this, you have to use inverse operations on both sides of the equation. 3-3=0 2-3=-1 X=-1 5. How to Write and Solve One-Step multiplication and Division Equations How To: Example: 1. First, to write an equation, you begin with the variable. 1=1 - -•X 4 3 2. Then, look at what numbers are negative vs. positive, and multiply or divide them by x or multiply/divide x by them. 1 =1 3 x. 4 3. To solve, you have to isolate the variable. To do this, you have to use inverse operations on both sides of the equation. 6. How to Write a Two-Step Equation How To: Example: 1. First, you begin with the variable. A number divided by 5, then added to 3. This equals 8. 2. Then, you add, subtract, multiply or divide numbers from or by the variable based on the wording.(see chart in beginning of presentation) X. + 3 = 8 — 5 3. Lastly, you compile your equation/expression. 5 • x =5 • 5 5 x=25 7. How to Write a Verbal Description of a Two-Step Equation How To: Example: 1. First, you write/say a situation in which these numbers are possible. (x•5)-4=11 2. Next, you present the variable and the operations and other numbers used, use key words from the chart in slide 1. 3. Lastly, present the final amount/answer. Amy is buying five apples. She has a discount of four dollars. If Amy's total is $11, then how much money was each Apple? X=3 8. How to Solve Two-Step Equations How To: Example: 1. First, you write an equation for the situation given. (x-3)•2=4 2. Then, to solve, you isolate the variable using inverse operations. With Two-Step equations, use the inverse of the addition/subtraction numeral first. 3. Make sure you use the inverse on both sides of the equation. 9. How to Solve Multi-Step Equations How To: 1. First, you write an equation for the situation given. 2. Then, combine like-terms. 3. Then, to solve, you isolate the variable using inverse operations. With Multi-Step equations, use the inverse of the addition/subtraction numerals first. 4. Make sure you use the inverse on both sides of the equation. Example: 12c+4c=48