Transcript Solving two step equations

Warm-up
1. x  5.7  9.2
The inverse operation
x of5.7
 5.7 
addition
is 9.2  5.7
subtraction
x  3.5
2.
m
 14
2.5
The inverse
m operation
2.5 
 14  2.5
of division
2.5
is multiplication
m  35
California
Standards
Preparation for 5.0 Students solve multistep
problems, including word problems, involving linear
equations and linear inequalities in one variable and
provide justification for each step.
How would we solve 3x + 5 = 12?
Let’s take another look at the
balance
3x + –5 5
12– 5
Subtract 5 from both sides
How would we solve 3x + 5 = 12?
Let’s take another look at the
balance
3x
7
Subtract 5 from both sides
Simplify
How would we solve 3x + 5 = 12?
Let’s take another look at the
balance
3x
3
7
3
Subtract 5 from both sides
Simplify
Divide both sides by
coefficient of the variable (3)
How would we solve 3x + 5 = 12?
Let’s take another look at the
balance
x
7
3
Subtract 5 from both sides
Simplify
7
SoDivide
the solution
is:
x

both sides by3
coefficient of the variable (3)
2x + 5 =11
–5 –5
2x = 6
Subtract 5 from both sides of the equation.
Divide both sides of the equation by 2.
x=3
The solution set is {3}.
Each time you perform an inverse operation, you
create an equation that is equivalent to the original
equation. Equivalent equations have the same
solutions, or the same solution set. In the example
above, 2x + 5 = 11, 2x = 6, and x = 3 are all
equivalent equations.
Let’s try one together.
Directions
Step 1. Undo addition/subtraction
Remember that whatever you do to
one side, you have to do to the
other!!!!******
Step 2. Undo multiplication/division.
Step 3. Solve for the variable.
3x + 4 = 25
-4 -4
0 21
3x = 21
3
3
x=7
Two step equations
Let’s try again.
-4
First: add or subtract.
Second : divide or multiply
Third: Is the variable
isolated?
7
1
-4
-7
y = -7 (7)
7
y = -49
Let’s try some more equations
Remember, we have to keep the equations
balanced!
Solve:
8m – 10 = 36
8m – 10 + 10 = 36 + 10
8m = 46
8
8
m = 23
4
w  17  31
6
w  17  17  31  17
6
w  14
6
6  w  6  14
6
w = 84
The Box Method
 Let’s try to solve backwards…
 6x – 11 = 13
×6
x
- 11
?
+ 11
÷6
4
X=4
13
24
13
Equations with Faction: Multiply by the least common
denominator (LCD) to clear fractions.
Multiply both sides by 8, the LCD of the fractions.
Distribute 8 on the left side.
y – 6 = 10
+6 +6
y = 16
Simplify. Since 6 is subtracted from y, add 6 to both
sides to undo the subtraction.
The solution set is {16}.
Now you try…
1. 3x – 7 = 2
x=3
2. 4x + 1 = -3
4.
y = 16
x = -1
5.
3. 5t – 2 = –32
t = –6
n=0
Challenge
1. 1.5 = 1.2y – 5.7
6=y
2. J
3. f
Application
Sara paid $15.95 to become a member at a gym. She
then paid a monthly membership fee. Her total
cost for 12 months was $735.95. How much was the
monthly fee?
1
Locate key words in the question. UNDERLINE WHAT
YOU ARE BEING ASKED TO FIND
The answer will be the monthly fee that Sara had paid
during the year.
2
Reread and circle relevant information
Sara paid $15.95 to become a member at a gym. She
then paid a monthly membership fee. Her total
cost for 12 months was $735.95. How much was the
monthly fee?
3
Reread the part of the problem you underlined,
and define an appropriate variable (or variables)
Let m represent the monthly fee that Sara paid.
4
Write an equation (or inequality) and then check
to see if it’s correct by rereading the circled and
underlined information
Sara paid $15.95 to become a member at a gym. She
then paid a monthly membership fee. Her total
cost for 12 months was $735.95. How much was the
monthly fee?
Circled info:
M = monthly fee
Sara paid that fee for 12 months.
She must also add the cost of the membership
Monthly fee
12m
plus
+
initial fee
15.95
is
=
total cost.
735.95
4
Solve the equation
12m + 15.95 = 735.95
–15.95 –15.95
12m
= 720.00
Since 15.95 is added to 12m,
subtract 15.95 from both sides
to undo the addition.
Since m is multiplied by 12,
divide both sides by 12 to
undo the multiplication.
m = $60 month
Check your answer
12m + 15.95 = 735.95
12(60) + 15.95 = 735.95
720+ 15.95 = 735.95
735.95 = 735.95
Lynda has 12 records in her collection. She adds the
same number of new records to her collection each
month. After 7 months Lynda has 26 records. How many
records does Lynda add each month?
r = 2 records a month
Lesson Quiz
Solve each equation.
1. 4y + 8 = 2
2. 3 + 2x = 11
3.
4.
4
–8
5. Nancy bought 5 rolls of color film and 6 rolls of blackand-white film. The 5 rolls of color film cost $15, and
Nancy’s total was $39. Write and solve an equation to
find the cost of one roll of black-and-white film.
6b + 15 = 39; $4