Transcript 3.6 ppt
Do Now: Create the word problem and solve for the variable. Fifteen less than 4 times a number is greater than 8. Ms. Ramsel wants to buy her classes’ favorite songs on itunes as a reward. Each song costs $1.29. She also has a discount card for $5 off her purchase. She wants to spend no more than $10. What is the greatest number of songs she can buy? Agenda Do Now Homework collection Notes Reward Practice Exit Ticket Clean Up Start the day on a positive! Know what? You’re pretty great. We have a big test coming up, so let me know if you’d like: Help preparing/studying Questions about how to create an extra credit study guide Questions off any parts of the past unit Review: Inverse Inverse: ONLY for OPPOSITE sides of the equation. To cancel things out. Taking away things you have multiples of. + = + Review: Inverse Inverse: ONLY for OPPOSITE sides of the equation. To cancel things out. Taking away things you have multiples of. 3 + 2y = – 7 -3 -3 2y = - 10 ¸2 __¸ 2 y = -5 Review: Combining Combining: ONLY for SAME side of the equation, or for expressions. Putting together similar terms on the same side. + + = + EQUALS + = + Review: Combining Combining: ONLY for SAME side of the equation, or for expressions. Putting together similar terms on the same side. 3z + 4 + 5z = 16r (3 + 5)z + 4 = 16r 8z + 4 = 16r Solving equations/inequalities with variables on both sides Combine like terms on the left side Combine like terms on the right side Use the inverse to combine like terms across the equal sign Solve for the variable Check your work Solving equations with variables on both sides Combine like terms on the left side Combine like terms on the right side Use the inverse to combine like terms across the equal sign Solve for the variable Check your work 4x + 3 = 18x – 5 -3 -3 4x = 18x – 8 -18x -18x -14x = -8 /-14 /-14 x = 8/14 You try: Solve for x Combine like terms on the left side Combine like terms on the right side Use the inverse to combine like terms across the equal sign Solve for the variable Check your work 3x – 17 = 27 - 2x You try: Solve for x Combine like terms on the left side Combine like terms on the right side Use the inverse to combine like terms across the equal sign 3x – 17 = 27 - 2x +2x + 2x 5x - 17 = 27 + 17 + 17 5x = 44 Solve for the variable /5 Check your work x = 8.8 /5 Solve. 1) 4x – 3 = -2 + 7x 4) 4x – 24 < 48 + 2x 2) 3x – 14 > -15 + 2x 5) 3x + 2 = -4 + 8x 3) 5 – 13x = -2 + 3x 6) 25x – 4 = -15 - 3 Solve. 1) 4x – 3 = -2 + 7x X = 1/3 2) 3x – 14 > -15 + 2x X > -1 3) 5 – 13x = -2 + 3x X = 7/16 4) 4x – 24 < 48 + 2x X < 36 5) 3x + 2 = -4 + 8x X = 6/5 6) 25x – 4 = -15x – 3 X = 14/25 But what if… An equation has no solution if no value makes the equation true. An equation is an identity equation if any value makes the equation true. Solve: Solve: 6m – 5 = 7m + 7 –m 10 – 8a = 2(5-4a) 6m-5 = 6m + 7 10 – 8a=10 – 8a -5 = 7, no solution 10=10, identity, always true WORD PROBLEMS!!!! YAAAAAAAAAAYYYYYY!!! LET’s practice word problems!!!!!! Word problems: Example 1 Your class hopes to collect 1,200 returnable bottles to raise money for a class trip. During the first week, the 24 students in your class collect an average of 34 bottles each. How many more bottles per student should the class collect? B = number of additional bottles per student 24(34 + b) = 1,200 816+ 24b = 1,200 -816 -816 24b = 384 ÷ 24 ÷24 b = 16 Each student needs to collect an additional 16 bottles. Word problems: Example 2 Your class goes to an amusement park. Admission is $10 for each student and $15 for each chaperone. The total cost is $380. There are 12 girls in your class and 6 chaperones on the trip. How many boys are in your class? X = number of boys in my class 10 (x + 12) + 6(15) = 380 10x + 120 + 90 = 380 10x + (120 + 90) = 380 10x + 210 = 380 - 210 - 210 10x = 170 ÷ 10 ÷ 10 x = 17 10(17 + 12) + 90 = 380? Yes . You try: create the equation and solve For Valentine’s day, Ashley must send 100 valentines. She can stuff 4 envelopes in a minute and has already completed 15. How many minutes will it take Ashley to complete this task? You try: create the equation and solve For Valentine’s day, Ashley must send 100 valentines. She can stuff 4 envelopes in a minute and has already completed 15. How many minutes will it take Ashley to complete this task? M = number of minutes to complete 4x + 15 = 100 -15 -15 4x = 85 ÷4 ÷4 x = 21.25 It will take Ashley 21.25 minutes to stuff all her envelopes. Now Try: write the equation, solve, and check. 1. When McKayla babysits, she charges $5 per hour for the first 4 hours, and then $8 per hour for each additional hour. How many hours did she babysit for if she earned $44? 2. The attendance at a ball game was 400 people. Student tickets cost $2 and adults tickets cost $3. If $1050 was collected in ticket sales, how many of each type of ticket were sold?