How can you use algebra tiles to solve addition or subtraction equations?
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1 . Solving Equations Using Addition or Subtraction How can you use algebra tiles to solve addition or subtraction equations? ACTIVITY: Solving Equations Work with a partner. Use algebra tiles to model and solve the equation. a. x = 4 Model the equation x = 4. To get the variable tile by itself, remove the tiles on the left side by adding tiles to each side. How many zero pairs can you remove from each side? Circle them. The remaining tile shows the value of x. So, x =. b. z 6 = c. p 7 = d. 5 = t 5 ACTIVITY: Solving Equations Work with a partner. Use algebra tiles to model and solve the equation. a. 5 = n + Solving Equations In this lesson, you will write simple equations. solve equations using addition or subtraction. solve real-life problems. Model the equation 5 = n +. Remove the by adding tiles on the right side tiles to each side. How many zero pairs can you remove from the right side? Circle them. The remaining tiles show the value of n. So, n =. b. y + 0 = 5 c. 7 + b = d. 8 = + z 96 Chapter Expressions and Equations
2 Math Practice Interpret Results How can you add tiles to make zero pairs? Explain how this helps you solve the equation. ACTIVITY: Writing and Solving Equations Work with a partner. Write an equation shown by the algebra tiles. Then solve. a. b. c. d. 4 ACTIVITY: Using a Different Method to Find a Solution Work with a partner. The melting point of a solid is the temperature at which the solid melts to become a liquid. The melting point of the element bromine is about 9 F. This is about 57 F more than the melting point of mercury. a. Which of the following equations can you use to find the melting point of mercury? What is the melting point of mercury? x + 57 = 9 x 57 = 9 x + 9 = 57 x + 9 = 57 b. CHOOSE TOOLS How can you solve this problem without using an equation? Explain. How are these two methods related? 5. IN YOUR OWN WORDS How can you use algebra tiles to solve addition or subtraction equations? Give an example of each. 6. STRUCTURE Explain how you could use inverse operations to solve addition or subtraction equations without using algebra tiles. 7. What makes the cartoon funny? 8. The word variable comes from the word vary. For example, the temperature in Maine varies a lot from winter to summer. Dear Sir: Yesterday you said x =. Today you are saying x =. Please make up your mind. Write two other English sentences that use the word vary. Use what you learned about solving addition or subtraction equations to complete Exercises 5 8 on page 00. Section. Solving Equations Using Addition or Subtraction 97
3 . Lesson Lesson Tutorials Key Vocabulary equivalent equations, p. 98 Two equations are equivalent equations if they have the same solutions. The Addition and Subtraction Properties of Equality can be used to write equivalent equations. Addition Property of Equality Words Adding the same number to each side of an equation produces an equivalent equation. Algebra If a = b, then a + c = b + c. Remember Addition and subtraction are inverse operations. Subtraction Property of Equality Words Subtracting the same number from each side of an equation produces an equivalent equation. Algebra If a = b, then a c = b c. EXAMPLE Solving Equations a. Solve x 5 =. Undo the subtraction. x 5 = Write the equation Addition Property of Equality x = 4 Simplify. The solution is x = 4. Check x 5 = 4 5 =? = b. Solve z + =. z + = Write the equation. Check Undo the addition. z = Subtraction Property of Equality Simplify. The solution is z =. z + = + =? = Exercises 5 0 Solve the equation. Check your solution.. p 5 =. w +. = 0.4. x 5 6 = 6 98 Chapter Expressions and Equations
4 EXAMPLE Writing an Equation A company has a profit of $750 this week. This profit is $900 more than the profit P last week. Which equation can be used to find P? A 750 = 900 P B 750 = P C 900 = P 750 D 900 = P Words The profit this week is $900 more than the profit last week. Equation 750 = P The equation is 750 = P The correct answer is B. Exercises 5 4. A company has a profit of $0.50 today. This profit is $45.5 less than the profit P yesterday. Write an equation that can be used to find P. EXAMPLE Real-Life Application Video Game Scoring The line graph shows the scoring while you and your friend played a video game. Write and solve an equation to find your score after Level 4. Score (points) You Your Friend points (4, 8) You can determine the following from the graph. Words Your friend s score is points less than your score. Variable Let s be your score after Level 4. Level Equation 8 = s 8 = s Write equation. + + Addition Property of Equality 5 = s Simplify. Your score after Level 4 is 5 points. Reasonable? From the graph, your score after Level 4 is between 0 points and 0 points. So, 5 points is a reasonable answer. 5. WHAT IF? You have points after Level. Your score is 7 points less than your friend s score. What is your friend s score? Section. Solving Equations Using Addition or Subtraction 99
5 . Exercises Help with Homework. VOCABULARY What property would you use to solve m + 6 = 4?. VOCABULARY Name two inverse operations.. WRITING Are the equations m + = 5 and m = equivalent? Explain. 4. WHICH ONE DOESN T BELONG? Which equation does not belong with the other three? Explain your reasoning. x + = x + = 5 x = 6 x 9 = 9+(-6)= +(-)= 4+(-9)= 9+(-)= Solve the equation. Check your solution. 5. a 6 = 6. = z = k x + 4 = 4 9. c 7.6 = = w = q +. p 6 =. g 9 = = d y =.5 6. x 5. = q = = r w + 8 = k =. ERROR ANALYSIS Describe and correct the error in finding the solution. x + 8 = x = 8 Write the word sentence as an equation. Then solve.. 4 less than a number n is more than a number c is. 4. The sum of a number y and is The difference between a number p and 6 is 4. In Exercises 6 8, write an equation. Then solve. 6. DRY ICE The temperature of dry ice is 09. F. This is 84.9 F less than the outside temperature. What is the outside temperature? 7. PROFIT A company makes a profit of $.8 million. This is $.54 million more than last year. What was the profit last year? 8. HELICOPTER The difference in elevation of a helicopter and a submarine is 8 meters. The elevation of the submarine is 7 meters. What is the 4 elevation of the helicopter? 00 Chapter Expressions and Equations
6 GEOMETRY Write and solve an equation to find the unknown side length. 9. Perimeter = cm 0. Perimeter = 4. in.. Perimeter = 4.6 ft? 5 cm cm? 8. in. In Exercises 6, write an equation. Then solve. 8. in.?.8 in. 5. ft. STATUE OF LIBERTY The total height of the Statue of Liberty and its pedestal is 5 feet more than the height of the statue. What is the height of the statue?. ft 6.4 ft 05 ft. BUNGEE JUMPING Your first jump is 50 feet higher than your second 6 jump. Your first jump reaches 00 feet. What is the height of your 5 second jump? 4. TRAVEL Boatesville is 65 kilometers from Stanton. A bus traveling from 5 Stanton is 4 kilometers from Boatesville. How far has the bus traveled? 5. GEOMETRY The sum of the measures of the angles of a triangle equals 80. What is the measure of the missing angle? 0. m SKATEBOARDING The table shows your scores in a skateboarding competition. The leader has.6 points. What score do you need in the fourth round to win? 7. CRITICAL THINKING Find the value of x when x + 6 =. Find the values of x. Round 4 Points ? 8. x = 9. x = x + 5 = 8 Multiply or divide. (Section.4 and Section.5) ( ) 4. 8 ( ) MULTIPLE CHOICE A class of 44 students voted for a class president. Three-fourths of the students voted for you. Of the students who voted for you, 5 are female. How 9 many female students voted for you? (Section.4) A 50 B 60 C 80 D 08 Section. Solving Equations Using Addition or Subtraction 0
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