Solve 0.5 + 0.3y = 0.7y 0.3 0.5 + 0.3y = 0.7y 0.3 0.3y 0.3y 0.5 = 0.4y 0.3 +0.3 + 0.3 0.8 = 0.4y 2 = y To collect the variable terms on one side, subtract 0.3y from both sides. Since 0.3 is subtracted from 0.4y, add 0.3 to both sides to undo the subtraction. Since y is multiplied by 0.4, divide both sides by 0.4 to undo the multiplication.
Tuesday Homework: 1.3 textbook pg. 23 #6, 7, 8, 15, 17, 18, 19, 20, 24, & 26 1 st : Put your homework corrections from Friday in yellow folder 2 nd : Turn in missing assignment forms with parent signatures 2 nd : Take out planner, spiral, and math facts 3 rd : Complete warm up on a white board, Do not erase until Mrs. Daggert or Miss. Bibb checks your work 4 th : After you finish your warm up, practice math facts
Dress code Plan for this week: Tuesday: 1.3 Equations: No solution, One solution, infinite solutions Wednesday: 1.3 distributive property on both sides Thursday: 1.3 fraction equations Friday: Lesson 1.4- Rewriting Equations
Challenge Last Week Confusing Ms. Hamiltonian Name Subject Form of Communication June Spanish Email Kris Math Texting Marcus Science Letters Harriet Music Phone Calls
Challenge of the Week Find the digits a, b, and c for which the following subtraction problem of 3-digit numbers is true: 7a2-48b=c73
1.3 No solution, One Solution, Infinite Solution Equations Essential Question: How can you recognize what type of solution an equation has?
Jon and Sara are planting tulip bulbs. Jon has planted 60 bulbs and is planting at a rate of 44 bulbs per hour. Sara has planted 96 bulbs and is planting at a rate of 32 bulbs per hour. In how many hours will Jon and Sara have planted the same number of bulbs? How many bulbs will that be? Sentence: Import Info: Person Bulbs Jon Sara Equation: 60 bulbs plus 44 bulbs per hour 96 bulbs plus 32 bulbs per hour
Application Continued b = 3 Let b represent bulbs, and write expressions for the number of bulbs planted. 44 32 the 60 bulbs plus bulbs 96 bulbs When is same each bulbs plus? each as hour hour 60 + 44b = 96 + 32b 60 + 44b = 96 + 32b 32b 32b 60 + 12b = 96 60 60 To collect the variable terms on one side, subtract 32b from both sides.
Application Continued After 3 hours, Jon and Sara will have planted the same number of bulbs. To find how many bulbs they will have planted in 3 hours, evaluate either expression for b = 3: 60 + 44b = 60 + 44(3) = 60 + 132 = 192 96 + 32b = 96 + 32(3) = 96 + 96 = 192 After 3 hours, Jon and Sara will each have planted 192 bulbs.
A painting company charges $250 base plus $16 per hour. Another painting company charges $210 base plus $18 per hour. How long is a job for which the two companies costs are the same? 20 hours Sentence: Import Info: Equation:
1 st : solve for variable WORDS Look to see if you can isolate variable The variable has only one solution NUMBERS ALGEBRA One Solution Equations 3 + 3 = 2(3) 6 = 6 3 + x = 2x x x 3 = x
WORDS NUMBERS ALGEBRA Infinite Solutions 1 st : simplify EACH side of the equation Look for on Each Side: Same coefficients on variable AND Same Constant 2 + 1 = 2 + 1 3 = 3 2 + x = 2 + x x x 2 = 2
1 st : simplify both sides of the equation Look for on Each Side: WORDS Same coefficients on variable AND NUMBERS No Solution Equations Different Constants 1 = 1 + 2 1 = 3 ALGEBRA x = x + 3 x x 0 = 3
Infinitely Solutions or No Solutions or 1 Solution Solve 10 5x + 1 = 7x + 11 12x. 10 5x + 1 = 7x + 11 12x 10 5x + 1 = 7x + 11 12x Identify like terms. 11 5x = 11 5x + 5x + 5x 11 = 11 Combine like terms on the left and the right. Add 5x to both sides. True statement. The equation 10 5x + 1 = 7x + 11 12x is an identity. All values of x will make the equation true. All real numbers are solutions.
Infinitely Solutions or No Solutions or 1 Solution Solve 12x 3 + x = 5x 4 + 8x 12x 3 + x = 5x 4 + 8x 12x 3 + x = 5x 4 + 8x Identify like terms. 13x 3 = 13x 4 13x 13x 3 = 4 Combine like terms on the left and the right. Subtract 13x from both sides. False statement. The equation 12x 3 + x = 5x 4 + 8x is a false equation. There is no value of x that will make the equation true. There are no solutions.
White Boards: Infinite, No Solutions, 1 Solution Solve 4y + 7 y = 10 + 3y 4y + 7 y = 10 + 3y 4y + 7 y = 10 + 3y 3y + 7 = 3y + 10 3y 3y 7 = 10 Identify like terms. Combine like terms on the left and the right. Subtract 3y from both sides. False statement. The equation 4y + 7 y = 10 + 3y is a false equation. There is no value of y that will make the equation true. There are no solutions.
Wednesday Homework: Weekly Review Sheet and 1.3 textbook pg. 23 # 10, 11, 12, 13, 16, 22, 25, 28, 29, & 30 1 st : Put your homework & Tuesday corrections in yellow folder 2 nd : Take out planner, spiral, and math facts 3 rd : Warm Up sheet in 4 squares. After you finish warm up do math facts Identify the Vocabulary: Are 5x 2 and 2x like terms? Why or why not? Identify the Distributive Property: What does it mean for a equation to have no solution? 10y (4y + 8) = 20
Dress Code Homework: Grading & Questions (use answer generator online)
1.3 Distributive Property Equations with Variables on Both Sides: Essential Question: What order of operations do you need to follow to solve equations with distributive property on both sides?
Infinitely Solutions or No Solutions or 1 Solution Solve 4 6a + 4a = 1 5(7 2a) 4 6a + 4a = 1 5(7 2a) Distribute 5 to the expression in parentheses. 4 6a + 4a = 1 5(7) 5( 2a) 4 6a + 4a = 1 35 + 10a 4 2a = 36 + 10a +36 +36 40 2a = 10a + 2a +2a 40 12a 40 = 12a Combine like terms. Since 36 is added to 10a, add 36 to both sides. To collect the variable terms on one side, add 2a to both sides.
White Boards: Infinite, No Solutions, 1 Solution Solve 3x + 15 9 = 2(x + 2). 3x + 15 9 = 2(x + 2) Distribute 2 to the expression in parentheses. 3x + 15 9 = 2(x) + 2(2) 3x + 15 9 = 2x + 4 3x + 6 = 2x + 4 2x 2x x + 6 = 4 6 6 x = 2 Combine like terms. To collect the variable terms on one side, subtract 2x from both sides. Since 6 is added to x, subtract 6 from both sides to undo the addition.
Thursday Homework: 1.3 Record and Practice Journal pg.14 1 st : Put your homework, Wednesday Corrections and Weekly Review Sheet in the yellow folder 2 nd : Take out planner, spiral, and math facts 3 rd : Warm Up sheet in 4 squares. After you finish warm up do math facts
Dress Code Homework: Grading & Questions (continue on from yesterday s notes) Highlight important info from yesterday s notes. In the left column write yourself 2 questions that you may see on the test next week.
Infinitely Solutions or No Solutions or 1 Solution Solve 1 Distribute to the expression in 2 parentheses. 3 = b 1 + 1 + 1 4 = b To collect the variable terms on one side, subtract 1 b from 2 both sides. Since 1 is subtracted from b, add 1 to both sides.
White Boards: Infinite, No Solutions, 1 Solution
White Boards: Application Four times Greg's age, decreased by 3 is equal to 3 times Greg's age increased by 7. How old is Greg? Sentence for Question: Important Info: Equation: Let g represent Greg's age, and write expressions for his age. four times Greg's age decreased by 3 is equal to three times Greg's age increased by 7. 4g 3 = 3g + 7
White Board Continued 4g 3 = 3g + 7 3g 3g g 3 = 7 + 3 + 3 g = 10 To collect the variable terms on one side, subtract 3g from both sides. Since 3 is subtracted from g, add 3 to both sides. Greg is 10 years old.
Solve each equation. Additional Practice 1. 7x + 2 = 5x + 8 3 2. (2x 5) = 5x + 4 8 3. 6 7(a + 1) = 3(2 a) 4. 4(3x + 1) 7x = 6 + 5x 2 all real numbers 5. 1 6. A painting company charges $250 base plus $16 per hour. Another painting company charges $210 base plus $18 per hour. How long is a job for which the two companies costs are the same? 20 hours