VIEWS: 5 PAGES: 20 POSTED ON: 7/14/2012 Public Domain
Algebra The beginnings of a continual math adventure. How are equations solved using the Subtraction and Addition Properties of Equality? Inverse Operations Inverse, or opposite, operations – Add/Subtract – Multiply/Divide – Square/square root Inverse operations “undo” each other. Subtraction Property of Equality If you subtract the same number from each side of an equation, the two sides remain equal. x+2=3 -2 -2 x=1 Addition Property of Equality If you add the same number to each side of an equation, the two sides remain equal. x-2=4 +2 +2 x=6 Balancing Equations The equal sign divides the equation into 2 sides. Both sides of the equation must remain equal or balanced. The Golden Rule of solving equations: What you do to one side, you MUST do to the other side. Examples x-2=1 x+4=9 +2 +2 -4 -4 x=3 x=5 Check: 3-2=1 Check: 5+4=9 1=1 9=9 Your Turn to Practice: Solving Addition and Subtraction Equations P. 46 Your Turn (a – f) Be sure to check your solution. Word Problem Example Tiger Woods won the 2002 Masters Championship with a final score of 12 under par, or -12. His scores for the first three rounds were -2, -3, and -6. What was his score for the fourth round? (-2)+(-3)+(-6)+s=(-12) Combine like terms (-11)+s=(-12) +11 +11 s=(-1) He needs to score 1 under par for the 4th round. Summarizer Suppose your friend was absent the day we reviewed solving addition and subtraction equations. Write a letter to your friend, in two paragraphs, explaining how to solve the two following equations: 62 = f – 14 y + 12 = -3 The following words or phrases must be included in your paragraph: solve -Subtraction Property of Equality Inverse operation Addition Property of Equality balance Solving Multiplication and Division Equations How are equations solved using the Division and Multiplication Properties of Equality? Division Property of Equality If you divide each side of an equation by the same nonzero number, the two sides remain equal. 2x= (-6) 2 2 x=(-3) Check: 2(-3)=(-6) -6 = -6 Your Turn P. 50 (a-c) Word Problem Example The tortoise is one of the slowest land animals, reaching a top speed of about 0.25 mile per hour. At this speed, how long will it take a tortoise to travel 1.5 miles? Distance=rate * time 1.5=0.25t At this speed, it would take a tortoise ___ hours to travel 1.5 miles. Solving Division Equations What is the opposite of division? Multiplication Property of Equality: If you multiply each side of an equation by the same number, the two sides remain equal. a = -7 To Check: -3 a = 21 -3 * a = -7 * -3 21 = -7 1 -3 -3 a = 21 -7 = -7 Your Turn P. 51 (d – f). Summarizer Keeping in mind what you have reviewed today, consider the following equation: 10x – 2 = 28. Create a flow map demonstrating how to solve this two-step equation. Place the equation in the first square then place one step in each square. The final square should contain the solution. The Next Step Now that you know how to solve one-step equations… You will combine this knowledge to solve two-step equations Two Step Equations A problem with two different operations Follow the order of operations backwards to solve—”Undo” the order of operations Compare What you KNOW NEW STUFF 2(3)+4 2x+4=10 1st: Multiply 1st: “undo” Add 6+4 2x+4=10 2nd: Add -4 -4 Answer: 10 2x=6 2nd: “undo” Multiply 2x=6 /2 /2 x=3 Analogy Think about wanting 2x-3=1 to interview the man 1st: get rid of child of the house alone – 2x-3=1 1st: Get rid of the child – +3 +3 – the addition or – 2x=4 subtraction part of the 2nd: get rid of spouse problem – 2x=4 2nd:Get rid of the – /2 /2 spouse – x=2 – the multiplication or division part of the Answer: x=2 problem Your Turn 4x+5=13 Answer: x=2 -3n-8=7 Answer: n=-5 1+2y=-3 Answer: y=-2 More Practice Workbook page 28