Chapter Solving Equations by Adding, Subtracting, Multiplying, and Dividing.notebook

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1 Bellwork: Write as a fraction and reduce if you can: 1) 2.7 2) Homework Questions??? Write each as a decimal, use repeating decimals when necessary: 3) 5/2 4) 6/8 Evaluate: 5) 2x + y; x = 4, y = 5 Aug 11 10:09 AM Aug 11 10:15 AM Vocabulary: Chapter 1.2 Solving Equations by Adding of Subtracting Solve one step equations in one variable by using addition or subtraction. Equations: mathematical statement that two expressions are equal Solution of an Equation: a value of the variable that makes the equation true. Aug 11 10:15 AM Aug 11 10:16 AM Think of Equations like scales, that show two quantities are equal. We solve equations by using inverse (opposite) operations. Inverse operations "undo" operations on the variable. What are the inverse operations of the following: Addition Subtraction Multiplication Division x + 5 = 10 Aug 11 10:18 AM Aug 12 8:06 AM 1

2 Solve each equation by using addition: Remember to keep the equation balanced by performing the same operation to both sides x = 21 Add x Check your solution, by substituting the value for the variable: Subtract x Solve Each Equation. Check your answer. Example 1: ¾ = t ¼ You Try 1: n 3.2 = 5.6 (21) 9 = = 12 Aug 11 10:20 AM Aug 11 3:12 PM Solving Equations by Using Subtraction: At times you will need to subtract to isolate the variable. Solve Each Equation. Check your answer. Example 2: 0.8 = m x = 6 Add x Check your answer: (6) + 8 = = 14 Subtract x You Try 2: d + 1 / 3 = 1 Aug 11 3:17 PM Aug 11 3:27 PM Remember; subtracting it the same as adding the opposite. At times it may be easier to add the opposite to both sides instead of subtracting. Solve each equation. Check your answer. Example 3: m = a = 9 Check 6 + (9) = 3 3 = 3 The opposite of 6 is 6. You Try 5: 3/4 + z = 5/4 Aug 11 3:29 PM Aug 11 3:44 PM 2

3 Addition Property of Equality Subtraction Property of Equality Properties of Equality words numbers algebra You can add the same number to both sides of an equation, and the statement will still be true. You can subtract the same number from both sides of an equation, and the statement will still be true. 3 = = = 5 7 = = 7 5 a + c = b + c a c = b c Application: A person's maximum heart rate is the highest rate, in beats per minute, that person's heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find the maximum heart rate of a 15 year old. Aug 11 3:47 PM Aug 11 3:53 PM Solving Equations by Using Multiplication: Chapter 1.3 Solving Equations by Multiplying of Dividing Solve one step equations in one variable by using multiplication of division. Keep the equation balanced while using inverse operations. Check answer Aug 12 7:58 AM Aug 12 7:58 AM Solve each equation. Check your answer. Example 1: Solving Equations by using Division: Keep the equation balanced. You Try 1: 8x = 72 Check answer 8x = 72 8x = 72 8(9) = = 72 x = 9 Aug 12 7:59 AM Aug 12 7:59 AM 3

4 Solve each equation. Check your answers. Example 2: 15 = 4z You Try 3: 0.5x = 10 Solving Equations that contain Fractions: Remember that dividing is the same as multiplying by the reciprocal. 4 2 = 4(½) When solving equations with fractions is may be easier to multiply by the reciprocal instead of dividing. Check Answer Aug 12 8:00 AM Aug 12 8:01 AM Solve each Equation. Check you answers. Example 3: Properties of Equality You can multiply both Multiplication sides of an equation by the Property of Equality same number, and the statement will still be true words numbers algebra 6 = 6 6(3) = 6(3) 18 =18 ac = bc You Try 5: Division Property of Equality You can divide both sides of an equation by the same nonzero number, and the statement will still be true. 8 = = 8 4 a c = b c (c 0) Aug 12 8:01 AM Aug 12 8:02 AM Application: The distance in miles from the airport that a plane should begin descending, divided by 3 equals the plane's height above the ground in thousands of feet. If a plane is 10,000 feet above ground, write and solve an equation to find the distance at which the pilot should begin descending. Homework: P # 21 57, and P #19 47 (all odds) A plane began descending 45 miles from the airport. Use the equation above to find how high the plane was flying when the descent began. Aug 12 8:02 AM Aug 11 3:56 PM 4

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