Lesson 1.03 (Creating One-Variable Equations) NOTES
S.E.L.F.I.E.
"A checklist we use to help us solve word problems. As we complete each step, we can check off the box." S: "Search for important information." E: "Express unknowns using a variable." L: "Look for two equal quantities." F: "Find the solution." I: "Interpret the solution." E: "Explain and check all your answers."
Constraint:
"A condition that is set on a situation." Constraint: x = 7 7x + 12 = 61 7(7) + 12 = 61 49 + 12 = 61 61 = 61 --> Viable
EOC Practice: "Is the answer (constraint) x = 12 viable or non-viable?" 2(x + 9) = 38
2(x + 9) = 38 2(12 + 9) = 38 2(21) = 38 42 =/ 38 --> Non-viable solution
Riley and Francesca both commute to work. Riley's commute on the train takes 12 minutes more than one half as many minutes as Francesca's commute by car. It takes Riley 36 minutes to get to work. Write an equation to determine how many minutes it takes Francesca to get to work. 36 = 1/2x − 12 36 = 2x − 12 36 = 2x + 12 36 = 1/2x + 12
36 = 1/2x + 12
Is this equation viable?: 4x + 9 = 57
4x + 9 = 57 4x + 9 - 9 = 57 - 9 4x / 4= 48 / 4 x = 12 ~~~~~~~~~~~~~~~ 4x + 9 = 57 4(12) + 9 = 57 48 + 9 = 57 57 = 57 Yes, the equation is viable
Viable and Non-Viable:
Viable: "A possible solution to the question being asked." (The solution is valid). Non-Viable: "Not a possible solution to the question being asked." (The solution is not valid).
Is this equation non-viable?: Constraint: x = 12 (NOTE: THIS IS A CONSTRAINT. IT GIVES US THE VARIABLE TO FIND IF IT IS VIABLE OR NOT VIABLE. I will not make another card for a constraint because there is one here in this case and also in the other cards). 3x = 9
x = 12 3x = 9 3(12) = 9 38 =/ 9 The solution to this equation is non-viable.
Practice #1: "Keshawn and Denny are playing cards. Keshawn had 3 times as many points as Denny. They had 280 points altogether. How many points did Keshawn have?"
x = Denny's Points 3x = Keshawn's Points x + 3x = 280 4x = 280 4x/ 4 = 280 / 4 x = 70 ---------------------- 3x = 280 3(70) = 280 210 =/ 280 Keshawn's points were 210, while Denny's points were 70. 210 + 70 make up 280. 210 + 70 = 280. When you substitute the "x" for the 70, it will be shown as a viable solution.
"Lennon practices basketball in the driveway. The ball bounces away and Lennon goes to get it. Before stopping, the ball rolls 4 yards more than twice the length of Lennon's driveway. If the ball is 56 yards away, how long is Lennon's driveway."
x = Length of Lennon's Driveway 2x + 4 = 56 2x + 4 - 4= 56 - 4 2x/2 = 52/2 x = 26 ---------------------------------- 2(26) + 4 = 56 52 + 4 = 56 56 = 56 The solution "x = 26" is viable.
Benjamin's age is 6 years less than twice Lucas's age. If Benjamin is 12 years old, how old is Lucas? Choose the answer below that is a viable solution to this problem. 3 5 7 9
x = Lucas's age 2x - 6 = 12 2x - 6 + 6 = 12 + 6 2x = 18 2x/2 = 18/2 x = 9 The solution is viable NOTE: Go to the LL Slides in the USB for Lesson 1.03 for more practice.
