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1、,More Equations-West Pender Middle School更多的方程-西德中学,More Equations-West Pender Middle School更多的方程-西德中学More Equations-West Pender Middle School更多的方程-西德中学More EquationsSolving Multistep EquationsSome equations may have more than two steps to complete.You may have to simplify the equation first by comb
2、ining like terms or even remove fractions to make solving easier.Samantha and Rebecca want to rent sports equipment at the city park.Samantha wants to rent inline skates,and Rebecca wants to rent a motor scooter.How would you write an equation and solve the problem to find the total cost for a speci
3、fied number of hours.Lets take a look at how you would solve this problem.,More Equations,Solving Multistep Equations,Some equations may have more than two steps to complete.You may have to simplify the equation first by combining like terms or even remove fractions to make solving easier.,Samantha
4、and Rebecca want to rent sports equipment at the city park.Samantha wants to rent inline skates,and Rebecca wants to rent a motor scooter.How would you write an equation and solve the problem to find the total cost for a specified number of hours.Lets take a look at how you would solve this problem.
5、,Here is the cost for each of the activities the girls would like to rent.Lets look at each individually and then together.,Inline Skates$3.00 plus$1.50/hourc=3+1.50 xc=individual costx=number of hours rental,Motor scooter$10.00 plus$2.75/hourc=10+2.75xc=individual costx=number of hours rental,Indep
6、endent variable,Dependent variable,constant,Independent variable,Dependent variable,constant,Combined cost(C)Use the equation C=3+1.50 x+10+2.75x to answer each of the following questions.C=4.25x+13,How much would Samantha and Rebecca pay for 2 hours rental?How much would Samantha and Rebecca pay fo
7、r 3 hours rental?If their total rental cost is$38.50,for how many hours did they use the equipment?,Multistep Equations,Equations with Like TermsEquations that contain FractionsEquations with variables on both sides,Important!To solve multistep equations,first clear fractions and combine like terms.
8、Then add or subtract variables to both sides so that the variable is on one side only.,Multistep equationsSTEP 1:Clear fractionsSTEP 2:remove parenthesisSTEP 3:move all variables to one side of the equation.,Solving equations containing like terms,8x+6+3x 2=37 11x+4=37 Combine like terms 11x+4 4=37
9、4Subtraction Property of Equality 11x=33Division Property of Equality 11 11 x=3Remember to keep your equal signs lined up to prevent you from making a mistake.On the next slide we will check our answer by substituting for x.,Check your answer by substituting for x,8x+6+3x 2=378(3)+6+3(3)2=37 Substit
10、ute 3 for x 24+6+9 2=37 Combine like terms 37=37?True,Solve:1)8d 11+3d+2=132)8x 3x+2=-333)2y+5y+4=254)4x+8+7x-2x=895)30=7y 35+6y,Solving equations that contain fractions,5n+7=-3 Multiply both side by 4 to clear fractions 4 4 44 5n+7=-3 4 Multiply both sides by 4,Multiplication Property of Equality 4
11、 4 4 5n+7=-3Subtract 7 from both sides,Subtraction Property of Equality5n+7 7=-3 7 5n=-10Divide both sides by 5,Division Property of Equality 5 5 n=-2 Remember to go back an substitute for n,Solve:1)4 2p=6 5 5 52)9z+1=2 4 4 43)x+2=5 2 3 6,Solving equations with variables on both sides is similar to
12、solving an equation with a variable on only one side.,You can add or subtract a term containing a variable on both sides of an equation.2a+3=3a2a 2a+3=3a 2a Subtract 2a from both sides.3=a Remember to keep equal(=)signs lined up to prevent errors.Always go back and check each equation by substitutin
13、g the solution into the original equation.,Moving terms is just like moving a single number,you use the Properties of Equality.,Solving equations with variables on both sides.,4x 7=5+7x4x 4x-7=5+7x-4x Subtract 4x from both sides.-7=5+3x-7-5=5 5+3x Subtract 5 from both sides.-12=3x-12=3x Divide both
14、sides by 3.3 3-4=x Remember go back and substitute for x.,Remember,you can move a whole term.,Solve:1)5x+2=x+62)4y 2=6y+63)4(x-5)+2=x+34)4x 5+2x=13+9x 215)8x 3=15+5x,Both figures have the same perimeter.What is the perimeter.,Remember how to find the perimeter of a polygon?,Well,these two perimeters
15、 are the same.,Write an equation and solve the following problem.,Sam and Ted have the same number of baseball trading cards in their collection.Sam has 6 complete sets plus 2 individual cards,and Ted has 3 complete sets plus 20 individual cards.How many cards are in a complete set?Find three consec
16、utive whole numbers such that the sum of the first two numbers equals the third number.Hint:Let n represent the first number.),Solve and check.,6x+3x x+9=33-9=5x+21+3x4 2p=6 5 5 5y 3y+1=1 2 8 4 2,5y 2 8y=3128=10a 5a 2x+2=5 2 3 68)5n 2 8n=31,谢谢你的阅读,知识就是财富丰富你的人生,31、只有永远躺在泥坑里的人，才不会再掉进坑里。黑格尔32、希望的灯一旦熄灭，生活刹那间变成了一片黑暗。普列姆昌德33、希望是人生的乳母。科策布34、形成天才的决定因素应该是勤奋。郭沫若35、学到很多东西的诀窍，就是一下子不要学很多。洛克,
