Warm ups
x + 11 = 29
3
5x + 16 = 51
n – (-5) = 2
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
Use PEMDAS to simplify
15 + 7 – 9 – 3 = 10
the left side
22 – 9 – 3 = 10
13 – 3 = 10
10 = 10
TOO
1) 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
1st: Distribute
2nd: Combine like terms
3rd: Add/Subtract
4th: Multiply/Divide
Check your Answer!

5x – 2(3 + x) = 12, x = 6
5(6) – 2(3 + 6) = 12
No variables = No distributing!!
5(6) – 2(9) = 12
30 – 18 = 12
12 = 12
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+1
3= x+2
4= x+3
EXAMPLE 1
The sum of three consecutive integers is 105.
Find the numbers.
1st: x
2nd: x + 1
3rd: x + 2
“sum” means add
x = 34
x + 1 = 35
x + 2 = 36
x + x + 1 + x + 2 = 105
3x + 3 = 105
-3
-3
3x = 102
3
3
x = 34
Answer: 34, 35, 36
MORE CONSECUTIVE INTEGERS
Consecutive
Integers
1st:
2nd:
3rd:
4th:
x
x+1
x+2
x+3
.
.
.
Consecutive
Even Integers
1st:
2nd:
3rd:
4th:
x
x+2
x+4
x+6
.
.
.
Consecutive Odd
Integers
1st:
2nd:
3rd:
4th:
x
x+2
x+4
x+6
.
.
.
EXAMPLE 2
The sum of four consecutive even integers is
116. Find the numbers.
1st: x
2nd: x + 2
3rd: x + 4
4th: x + 6
x = 26
x + 2 = 28
x + 4 = 30
x + 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
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