Presentation on theme: "Solving Equations with Variables on both Sides."— Presentation transcript:
1 Solving Equations with Variables on both Sides. What you’ll learnTo solve equations with variables on both sides.To identify equations that are identities or haveno solution.Identity: an equation that is true for everypossible value of the variable.
2 What is the solution of 5x+2=2x+14 ? When you have variables in both sides you can usethe properties of equality and inverse operationsto write a series of simpler equivalents equations.What is the solution of 5x+2=2x+14 ?5x+2=2x+14Subtract 2x from each side-2x -2xSimplify3x+2=14Subtract 2 from each side-2 -2Simplify.Divide each side by 33x=123 3SimplifyX=4Check your answer: 5(4)+2=2(4)+14
3 Solve each equation. Check your answer. Your turnSolve each equation. Check your answer.a) 3x+4=5x-10Answer: x=7b) 5(y-4)=7(2y+1)Answer: Y=-3
4 + Let’s do a word problem = 1.5p=1.25p+8 You solve it It takes a graphic designer 1.5 hours to make one page ofa web site. Using new software, the designer could completeeach page in 1.25 hours, but it takes 8 hours to learn thesoftware. How many Web pages would the designer haveto make in order to save time using the new software?Design time with new softwareTime to learn the softwareCurrent design time+=Let’s p= the number of pages the designer needs to make1.5p=1.25p+8You solve itAnd the answer is p=32,it will take the designer the same amount of timeTo make 32 web pages using either software. The designerMust make 33 pgs or more in order to save time using the newSoftware.
5 0.10 c+15=0.15c+10 Your turn Answer: c=100 Pristine Printing will print business cards for $0.10 each plusa setup charge of $15. The Printing Place offers businesscards for $0.15 each with a setup charge of $10. What numberof business cards costs the same from either printer.0.10 c+15=0.15c+10Answer: c=100
6 Identities and Equations with no Solution What is the solution to each equation?Solve it by yourselfa)10x+12=2(5x+6) b) 9m-4=-3m+5+12m10x+12=10x+129m-4=9m+5-4=5Because this is always true.There are many solutions ofthe equation. The originalequation is an identity.Because -4=5,The original equation hasno solution.
7 Your turnMatch each equation with the appropriate numberof solutions ?3y-5=y+2y-92y+4=2(y+2)2y-4=3y-5Infinitely many solutionsOne solutionNo solution-5=94=41=y