Solving Equations with Variables on both Sides. n r a e l ’ll u o y What To solve equations with variables on both sides. To identify equations that are identities or have no solution. Identity: an equation that is true for every possible value of the variable.
When you have variables in both sides you can use the properties of equality and inverse operations to write a series of simpler equivalents equations. What is the solution of 5 x+2=2 x+14 ? 5 x+2=2 x+14 -2 x 3 x+2=14 -2 -2 3 x=12 3 3 X=4 Subtract 2 x from each side Simplify Subtract 2 from each side Simplify. Divide each side by 3 Simplify Check your answer: 5(4)+2=2(4)+14
Your turn Solve each equation. Check your answer. a) 3 x+4=5 x-10 b) 5(y-4)=7(2 y+1) Answer: x=7 Answer: Y=-3
Let’s do a word problem It takes a graphic designer 1. 5 hours to make one page of a web site. Using new software, the designer could complete each page in 1. 25 hours, but it takes 8 hours to learn the software. How many Web pages would the designer have to make in order to save time using the new software? Current design time = Design time with new software + Time to learn the software Let’s p= the number of pages the designer needs to make 1. 5 p=1. 25 p+8 You solve it And the answer is p=32, it will take the designer the same amount of time To make 32 web pages using either software. The designer Must make 33 pgs or more in order to save time using the new
Your turn Pristine Printing will print business cards for $0. 10 each plus a setup charge of $15. The Printing Place offers business cards for $0. 15 each with a setup charge of $10. What number of business cards costs the same from either printer. 0. 10 c+15=0. 15 c+10 Answer: c=100
Identities and Equations with no Solution What is the solution to each equation? Solve it by yourself a)10 x+12=2(5 x+6) 10 x+12=10 x+12 Because this is always true. There are many solutions of the equation. The original equation is an identity. b) 9 m-4=-3 m+5+12 m 9 m-4=9 m+5 -4=5 Because -4=5, The original equation has no solution.
Your turn Match each equation with the appropriate number of solutions ? 3 y-5=y+2 y-9 -5=9 2 y+4=2(y+2) Infinitely many solutions 4=4 One solution 2 y-4=3 y-5 1=y No solution
Claswork odd Homework even