Notes and Instruction

Solving Multi-Step Linear Equations

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

Here are some examples

1. 3(x – 3) = 6 3x – 9 = 6 + 9 + 9 3x = 15 3 3 x = 5

2. 12 = -4p – 8 + 8 + 8 20 = -4p -4 -4 p = -5

3. 4(2y – 1) = -2(4) 8y – 4 = -8 +4 +4 8y = -4 8 8 y = -0.5

4. 2(c + 3) = -122c + 6 = -12

- 6 -6 2c = -18 2 2 c = -9

5. ¼ x + 3 = 9 -3 -3 ¼ x = 6Use the reciprocal! Multiply both sides by

4/1 or 44( ¼ x) = 6(4) x = 24

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 +102x = 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 hasThen, 3x + 15 represents Joseph.x + (3x + 15) = 5434x + 15 = 543 - 15 - 154x = 528 4 4 x = 132Frank has 132 and Joseph has

411. (plug 132 in 3x + 15)

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 = 1Now, 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) = 824x – 6 = 82 + 6 +64x = 88 4 4 x = 22The side lengths are 22 units and 19

units (22 – 3).

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!

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!

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)= 1224x + 6 = 122 - 6 - 64x = 116 4 4 x = 29The 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) = 2193x + 6 = 219 - 6 - 63x = 213 3 3 x = 71The numbers are 71, 73, and

75.

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