Download Solving Multi-Step Equations (2-3)

Solving Multi-Step
Equations (2-3)
Objective: Solve equations
involving more than one
operation. Solve equations
involving consecutive
integers.
Solve Multi-Step Equations
• When an equation requires more
than one step to solve it, it is called
a multi-step equation.
• To solve these equations, we must
undo each operation by working
backward.
• To undo an equation, you must use
the order of operations in reverse.
Example 1
• Solve each equation. Check your
solution.
a. 2q + 11 = 3
-11 -11
2q = -8
2
2
q = -4
Check:
2q + 11 = 3
2(-4) + 11 = 3
-8 + 11 = 3
3=3 
Example 1
• Solve each equation. Check your
solution.
12 k  9
b.
= -2 • 12
1 12
k + 9 = -24
-9
-9
k = -33
Check:
k9
 2
12
33  9
 2
12
24
 2
12
-2 = -2 
Example 2
• Susan had a $10 coupon for the purchase of any item.
She bought a coat that was on sale for ½ its original price.
After using the coupon, Susan paid $125 for the coat
before taxes. What was the original price of the coat?
Write an equation for the problem. Then solve the
equation.
½ p – 10 = 125
+10 +10
2/ •½ p = 135 • 2
1
p = $270
Solve Consecutive Integer
Problems
• Consecutive integers are in counting
order, such as 4, 5, and 6 or n,
n + 1, and n + 2.
• Counting by two will result in
consecutive even integers if the
starting integer n is even and
consecutive odd integers if the
starting integer n is odd.
• Number theory is the study of
numbers and the relationships
between them.
Solve Consecutive Integer
Problems
Type
Consecutive
Integers
Words
Integers that
come in
counting
order.
Even integer
Consecutive followed by
Even Integers the next even
integer.
Consecutive
Odd Integers
Odd integer
followed by
the next odd
integer.
Symbols
Example
n, n + 1,
n + 2, . . .
. . ., -2, -1,
0, 1, 2, . . .
n, n + 2,
n + 4, . . .
. . ., -2, 0, 2,
4, 6, . . .
n, n + 2,
n + 4, . . .
. . ., -1, 1, 3,
5, 7, . . .
Example 3
• Write an equation for the following problem.
Then solve the equation and answer the
problem. Find three consecutive odd integers
with a sum of 57.
– First Integer = n
– Second Odd Integer = n + 2
– Third Odd Integer = n + 4
n + n + 2 + n + 4 = 57
3n + 6 = 57
-6 -6
3n = 51
3
3
n = 17
17, 19, 21
Check Your Progress
• Choose the best answer for the
following.
– Solve 6v + 7 = -5. Check your
solution.
6v + 7 = -5
A. v = -2
-7 -7
B. v = -6
6v = -12
C. v = 2
6
6
D. v = 1/3
6v + 7 = -5
6(-2) + 7 = -5
-12 + 7 = -5
-5 = -5 
Check Your Progress
• Choose the best answer for the
following.
4j  ( 4)
– Solve
= 12. Check the
6
solution.
6 4j  4
 12 • -6
A. j = 17
1
6
B. j = -17
-4j + 4 = -72
-4
-4
C. j = 19
-4j = -76
D. j = -19
4(19)  ( 4)
-4
-4
 12
6
76  4
72
 12
 12 12 = 12 
6
6
Check Your Progress
• Choose the best answer for the
following.
– Three-fourths of the difference of a
number and 7 is negative fifteen.
What is the number?
A.
B.
C.
D.
-13
-15
¾
7
4/
3
• ¾ (n – 7) = -15 • 4/3
n – 7 = -20
+7 +7
Check Your Progress
• Choose the best answer for the
following.
– Find three consecutive even integers
whose sum is 84.
A.
B.
C.
D.
28, 30, 32
26, 28, 30
20, 20, 24
40, 20, 24
n + n + 2 + n + 4 = 84
3n + 6 = 84
-6 -6
3n = 78
3
3
n = 26