Module 3 topic 2 notes
- 1. Module 3, Topic 2 Notes Solving Multi-Step Linear Equations
- 2. Solving Multi-Step Equations Is just like solving one-step equations with a few more steps…we still use inverse operations May require you to use the distributive property: -3(x + 7) = -3x – 21 May ask you to combine like terms: 3x + 5x = 8x Might have variables on both sides
- 3. Here are some examples 3(x – 3) = 6 3x – 9 = 6 + 9 + 9 3x = 15 3 3 x = 5 12 = -4p – 8 + 8 + 8 20 = -4p -4 -4 p = -5 2(y – 2) = -2(3y + 4) 2y – 4 = -6y – 8 +6y +6y 8y – 4 = -8 +4 +4 8y = -4 8 8 y = -0.5 8c + 6 = 6c – 12 -6c -6c 2c + 6 = -12 - 6 -6 2c = -18 2 2 c = -9
- 4. Just like before, you may have to write your own equations and then solve them! Translate the following statement into an equation and then solve. Ten less than twice a number is 36. Find the number. Let x = the missing number. 2x – 10 = 36 +10 +10 2x = 46 2 2 The number is 23. Joseph has fifteen more than three times as many baseball cards as Frank. If together they have a total of 543 cards, how many does each have? Let x = # of cards Frank has Then, 3x + 15 represents Joseph. x + (3x + 15) = 543 4x + 15 = 543 - 15 - 15 4x = 528 4 4 x = 132 Frank has 132 and Joseph has 411. (plug 132 in 3x + 15)
- 5. More Examples If 10 = 15 – 5k, find the value of 6 + 4k. First, solve the equation for k. 10 = 15 – 5k -15 -15 -5 = -5k -5 -5 k = 1 Now, substitute 1 for k in your expression: 6 + 4k = 6 + 4(1) = 10 The length of a rectangle is three less than its width. If the perimeter is 82, find the dimensions of the rectangle. Let x = the width. The length would be x – 3. Remember that we find perimeter by adding all the sides! x + x + (x – 3) + (x – 3) = 82 4x – 6 = 82 + 6 +6 4x = 88 4 4 x = 22 The side lengths are 22 units and 19 units (22 – 3).
- 6. Consecutive Integer Problems Consecutive integers are integers in order. For example: 1, 2, 3 -5, -4, -3 8, 9, 10 Examples of consecutive odd integers are 1, 3, 5 and 9, 11, 13 Examples of consecutive even integers are 2, 4, 6 and 20, 22, 24 ***We need a way to set these up as equations when we don’t know the first number in the list!
- 7. How to Set Up a Consecutive Integers Problem For three consecutive integers, use x, x + 1, x + 2 For three consecutive odd integers, use x, x + 2, x + 4 For three consecutive even integers, use x, x + 2, x + 4 **Some students say that odds should be x, x + 1, and x + 3…but remember odd numbers skip a number just like even numbers… so they’re the same!
- 8. Consecutive Integer Examples The sum of four consecutive integers is 122. Find the largest integer. Let x, x+1, x+2, and x+3 be your numbers. x +(x+1)+(x+2)+(x+3)= 122 4x + 6 = 122 - 6 - 6 4x = 116 4 4 x = 29 The numbers are 29, 30, 31, and 32. The largest is 32. The sum of three consecutive odd integers is 219. Find the integers. Let x, x+2, and x+4 be your numbers. x + (x+2) + (x+4) = 219 3x + 6 = 219 - 6 - 6 3x = 213 3 3 x = 71 The numbers are 71, 73, and 75.
- 9. Some Extra Practice for You! Solve multi-step equations to win a game: http://www.quia.com/rr/168572.html Here’s another equations and basketball game. This time, you’ll need two steps to solve the equations: http://www.math-play.com/Two-Step-Equations-Game.html