Solving Multi-Step Linear Equations and Simplifying Expressions
Learn how to solve multi-step linear equations using inverse operations and simplify expressions in this educational content. Check out examples and practice problems to enhance your understanding.
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Presentation Transcript
Warm Up Simplify the expression. 4) 2?2 ? 5?2 5? 2?2 6? 2?2+ 3? 1) 5) 2 2+ 5? + 2 2+ 9? 5?2 ? 2?2 5? 2) 6) 2?2+ 9?? + 3?2 2?? 4?2+ ? 6?2 5? 3)
Section 1.2: Solving Multi-Step Equations Students will solve multi- step linear equations using inverse operations. Students will use unit analysis to model real- life problems.
Example 1: Solve 2.5? 13 = 2 Ask yourself how am I going to isolate the variable. 2.5? 13 = 2 +13 +13 Add 13 to both sides. x is still not alone. 2.5? = 15 2.5 2.5? = 15 2.5 Divide both sides by 2.5 x=6 How do you think we will check this? Simplify your answer 2.5(6) 13 = 2
Ex 2: Solve for r. Check your solution. 15 = 1.5? + 3 15 = 1.5? + 3 -3 -3 12 1.5=1.5 Subtract 3 from both sides Divide by 1.5 from both sides 1.5? r= 8 Simplify your answer. Check your answer. 15 = 1.5(8) + 3
Ex 3: Solve and check your solution. 12 = 9? 6? + 15 What do you notice that is different about this equation? Combined like terms 12 = 9? 6? + 15 12 = 3? + 15 -15 -15 27 3? x=-9 Subtract 15 from both sides. 3=3 Divide both sides by 3 Simplify your answer Check your work. 12 = 9( 9) 6( 9) + 15 -12 = -12
Ex 4: Solve and check your solution. 5? + 4? 8 = 19
Try these 21 =1 2? + 3 = 9 2? 11 2x 10x + 12 = 18 n= -3 c= -20 x= -1/2
Using structure to Solve a Multi-Step Equation Ex1. Solve and check you work 2 1 ? + 3 = 8 Distribute the 2 (Distribute Property) 2 2? + 3 = 8 Combined like terms Subtract 5 from both sides 2? + 5 = 8 -5 -5 2 2? = 13 x= 13 2= 6.5 Divide both sides by -2 2 Simplified Check your answer. There is a second method to solve this. *Divide first
Ex. 2: Solve and check your answers. 4 ? 6 1 = 31 Show it both ways n=14
More Practice 3 ? + 1 + 6 = 9 4 2m + 5 3m = 35 Challenge yourself: 5 3 ? + 2 3 ? = 14 x=1
Ex 3: Understand the problem. How do we find the mean? 1. Make a plan. Use what we know about mean to solve the problem. 2. Use the table to find the number of miles x you need to bike on Friday so that the mean number of miles biked per a day is 5. Solve the problem. 3.5+5.5+0+5+? 5 3. =5 Days Monday Tuesday Wednesday Thursday Friday Miles 3.5 5.5 0 5 x 14+? 5 = 5 (5)14+? = 5(5) 5 14 + x = 25 -14 -14 X = 11 Look back. Does our answer make sense? 4.
Ex 4: Your school s drama club charges $4 per person for admission to play. The club borrowed $400 to pay for costumes and props. After paying back the loan, the club has a profit of $100. How many people attended the play? Understand the problem. What is important to us? What are we being asked? 1. Make a plan. How should we go about solving this? 2. Solve the problem. 4 x- 400= 100 How many people attended the play? Solve for x x= 125 Look back. What happens when we multiply 4 by 125? 3. 1. 1.
Try This You have 96 feet of fencing to enclose a rectangle pen for your dog. To provide sufficient running space for the dog to exercise, the pen should be three times as long as it is wide. Find the dimensions of the pen. 3x Understand the problem What do we know about a rectangle? 1. x Make a plan Draw a picture 2. Solve the problem 3x + x = 96 4x = 96 x= 24 24/2=12 Dimensions are 36 ft by 12 ft/ Look back Add 36+36+12+12= ??? 3. ***Remember perimeter = l+w+l+w=96 4.
