Lesson 22 ~ Expressions and Equations

Transcription

1 Lesson ~ Expressions and Equations Write an algebraic expression for each phrase. 1. the product of x and seven. the sum of 8 and p. two more than the product of y and four. the quotient of k and ten Evaluate each expression. 5. y + 6 when y = 1 6. x + when x = 5 7. m when = m 8. 5d when d = x + when x = 10..1w +. 5 when w = ( a + b) when a = and b = 9 1. y + 6x when x = and y = The fire department is having a BBQ fundraiser. The hot dogs costs $1.50 each and cans of soda cost $0.75 each. The department uses the algebraic expression 1.50x y to calculate customers total expenses. a. What does the x variable represent? b. What does the y variable represent? c. A family buys 7 hot dogs and sodas. What are their total expenses? Determine if the number given is the solution to the equation. p x = 19 Is the solution? = 1 Is 8 the solution? 16. y + 5 = 1 Is the solution? m 5.6 = Is the solution? 008 SM C Curriculum Oregon Focus on Rational Numbers & Equations

2 Lesson ~ Solving One-Step Equations Solve each equation using an equation mat or inverse operations. Check your solution. p 1. x + 7 = 11. y 1 =. 6 5 = = m 5. k = 1 6. h +.8 = 1. 9 d = 8. 7d = 9. x =. 10. = b f = = y = 11+ a 1. g 1 = y = Write an algebraic equation for each sentence. Solve each equation using an equation mat or inverse operations. 16. Six less than x equals twenty-two. 17. The quotient of y and four is negative ten. 18. Three-tenths times m is three and six tenths. 19. Seven less than h is negative nine. 0. Bryanna is thinking of two numbers. Their sum is 7. One of the numbers is 11. Write an equation and solve to find the other number. 008 SM C Curriculum Oregon Focus on Rational Numbers & Equations

3 Lesson ~ Solving Two-Step Equations Solve each equation for the variable. Show your work and check your solution. y 1. x + 6 =. 7 = = m h. +.5 = y + 1 = x 8 = 1 p 7. 1 = 9 1 w 8. d + 6 = = a = = 6x 1. y 1 = 1. Katrina bought a new sofa. She was able to pay $100 at the time she received the sofa. She will pay $ each month on the balance. The original cost of the sofa was $98. a. Let x represent the number of months needed to pay off the cost of the sofa. Explain how the equation x = 98 represents this situation. b. Solve the equation. How many months will it take Katrina to pay off the sofa? 1. Hank is thinking of a number. If he multiplies his number by seven and then adds 10, he gets 59. What is Hank s number? 008 SM C Curriculum Oregon Focus on Rational Numbers & Equations

4 Lesson 5 ~ The Distributive Property Use the Distributive Property to rewrite each expression without parentheses ( x + ). 5( y ). 7( m 1). 9 (x + ) 5. (7 + p) 6. 1 (8x 10) Solve each equation for the variable. Check your solution. 7. ( x + 7) = ( x ) = 9. 9 = ( x 11) (x ) = (8x + 0) = = 5( x 1) 1. (x 1) = 1. = ( x + 1) ( x + 1.1) = Jacob has kept a food journal of the last 1 days. He has eaten 00 calories less than his normal intake by not eating ice cream every night. He calculated that he has eaten 0,800 calories over the last 1 days. a. The equation 1 ( x 00) = 0800 represents this situation. What does x represent in the equation? b. Solve the equation and determine what Jacob s normal calorie intake was before he stopped eating ice cream. 008 SM C Curriculum Oregon Focus on Rational Numbers & Equations

5 Lesson 6 ~ Simplifying Expressions 1. Examine the expression 5x + 9 x 7 y. a. Which terms are like terms? b. What is the coefficient of the y term? c. Write the expression in simplified form. Simplify each algebraic expression.. y + 6x + 5x y. a + b + a + b a. 1 m + m 10 5m 5. 7( x + ) 0 6. h h 1+ h 7 7. ( y + 5) + y 8. ( p 1) + 9 p + 9. x + ( x + 5) ( m + 1) ( y ) 11y 1. 5( x + ) + ( x ) 1. g g ( g ) 008 SM C Curriculum Oregon Focus on Rational Numbers & Equations

6 Lesson 7 ~ Simplifying and Solving Equations Solve each equation for the variable. Show your work and check your solution x + x 6x =. 8 y + 5 y + 1 = 6. = 5( x + 8) +. m + ( m 8) = 1 5. p + p p + p = 8 6. ( y + 5) + y = h + h + h + = = ( k + ) + ( k ) 9. ( d + 1.) 1.8 = ( w + ) = Tyler told his friend this riddle: I am thinking of a number. Three times my number plus twice my number is twenty. What number am I thinking of? a. Write an equation that models Tyler s statement. b. Solve the equation. What number was Tyler thinking of? 008 SM C Curriculum Oregon Focus on Rational Numbers & Equations

7 Lesson 8 ~ Solving Equations with Variables on Both Sides Solve each equation for the variable. Show your work and check your solution. 1. y + 1 = 8y. x + 10 = 9x 6. 0 d = d. 1 p 7 = 6 p y 0 = y x = x h = h 8. m + 6 = 9m b = 5b x + = x NK Karate Club offers two different fees for their karate classes. Club members are charged a one-time membership fee of $ and pay $ per class. Non-members pay $8 per class. Let y represent the number of karate classes attended. a. Write an expression to represent the cost for a non-member to attend y classes. b. Write an expression to represent the cost for a member to attend y classes. c. Set the two expressions equal to each other and solve the equation to determine how many classes result in the same cost for a member and non-member. 008 SM C Curriculum Oregon Focus on Rational Numbers & Equations