Warm ups

x + 11 = 29 5x + 16 = 51 n – (-5) = 23 6 3

3-3 Multi-Step Equations

Objective: To combine like terms and solve

consecutive integers.

To Clarify . . .

Final answer MUST be in the form: letter = number

You may NOT write a decimal answer unless there were decimals in the original problem. Most answers will be either a whole number or a

reduced, improper fraction NO MIXED NUMBERS!!!

Example 1

5x + 7 – 3x – 3 = 10

2x + 4 = 10

- 4 - 4

2x = 6

2 2

x = 3

Same side of the equation, combine like terms

Check your Answer! Always check answer in the original

equation

5x + 7 – 3x – 3 = 10, x = 3

5(3) + 7 – 3(3) – 3 = 10

15 + 7 – 9 – 3 = 10

22 – 9 – 3 = 10

13 – 3 = 10

10 = 10

Use PEMDAS to simplify the left side

TOO1) x + x + 45 = 180

2) 4x – 3 – 6x = 15

3) 2x – x + 3 + 5 = 10

Answers:

1) x = 135/2

2) x = -9

3) x = 2

Example 2

5x – 2(3 + x) = 12

5x – 6 – 2x = 12

3x – 6 = 12

+ 6 + 6

3x = 18

3 3

x = 6

2nd: Combine like terms

1st: Distribute

3rd: Add/Subtract

4th: Multiply/Divide

Check your Answer!

5x – 2(3 + x) = 12, x = 6

5(6) – 2(3 + 6) = 12

5(6) – 2(9) = 12

30 – 18 = 12

12 = 12

No variables = No distributing!!

WHAT ARE CONSECUTIVE INTEGERS?

Numbers in a row:1,2,3,4

If I let x = 1, how could we represent “2” using “x”?2 = x + 13 = x + 24 = x + 3

EXAMPLE 1

1st: x2nd: x + 13rd: x + 2

“sum” means add

x = 34x + 1 = 35x + 2 = 36

x + x + 1 + x + 2 = 105

3x + 3 = 105

- 3 - 3

3x = 102

3 3

x = 34

Answer: 34, 35, 36

The sum of three consecutive integers is 105. Find the numbers.

MORE CONSECUTIVE INTEGERS

1st: x2nd: x + 13rd: x + 24th: x + 3

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.

.

1st: x2nd: x + 23rd: x + 44th: x + 6

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.

.

Consecutive Integers Consecutive Even Integers

Consecutive Odd Integers

1st: x2nd: x + 23rd: x + 44th: x + 6

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.

EXAMPLE 2

1st: x2nd: x + 23rd: x + 44th: x + 6

x = 26x + 2 = 28x + 4 = 30x + 6 = 32

x + x + 2 + x + 4 + x + 6 = 116

4x + 12 = 116

- 12 - 12

4x = 104

4 4

x = 26

Answer: 26, 28, 30, 32

The sum of four consecutive even integers is 116. Find the numbers.

TOO: WRITE AN EQUATION AND SOLVE with a partner

1) Find three consecutive integers whose sum is -48.

2) Find three consecutive odd integers whose sum is -27.

**Watch your signs**

Homework

3-3 Practice Worksheet