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More Equations
Solving Multistep Equations
Some equations may have more than two steps
to complete. You may have to simplify the
equation first by combining like terms or even
remove fractions to make solving easier.
Samantha and Rebecca want to rent sports
equipment at the city park. Samantha wants to
rent inline skates, and Rebecca wants to rent a
motor scooter.
How would you write an equation and solve the
problem to find the total cost for a specified
number of hours.
Let’s take a look at how you would solve this
problem.
Here is the cost for each of the activities the
girls would like to rent. Let’s look at each
individually and then together.
Inline Skates
$3.00 plus $1.50/hour
Dependent
variable
c = 3 + 1.50x
constant
Motor scooter
$10.00 plus $2.75/hour
Independent
variable
Independent
variable
c = 10 + 2.75x
Dependent
variable
c = individual cost
x = number of hours rental
constant
c = individual cost
x = number of hours rental
Combined cost (C)
Use the equation C = 3 + 1.50x + 10 + 2.75x to
answer each of the following questions.
C = 4.25x + 13
• How much would Samantha and Rebecca pay for 2
hours’ rental?
• How much would Samantha and Rebecca pay for 3
hours’ rental?
• If their total rental cost is $38.50, for how many
hours did they use the equipment?
Multistep Equations
Equations with Like Terms
Equations that contain Fractions
Equations with variables on both
sides
Important!
To solve multistep equations, first clear
fractions and combine like terms. Then add or
subtract variables to both sides so that the
variable is on one side only.
Multistep equations
STEP 1: Clear fractions
STEP 2: remove
parenthesis
STEP 3: move all
variables to one side of
the equation.
Solving equations containing like terms
8x + 6 + 3x – 2 = 37
11x + 4 = 37
11x + 4 – 4 = 37 – 4
11x = 33
11 11
x=3
Combine like terms
Subtraction Property of Equality
Division Property of Equality
Remember to keep your equal signs lined up to prevent you from
making a mistake. On the next slide we will check our answer by
substituting for x.
Check your answer by substituting for x
8x + 6 + 3x – 2 = 37
8(3) + 6 + 3(3) – 2 = 37 Substitute 3 for x
24 + 6 + 9 – 2 = 37 Combine like terms
37 = 37 ? True
Solve:
1) 8d – 11 + 3d + 2 = 13
2) 8x – 3x + 2 = -33
3) 2y + 5y + 4 = 25
4) 4x + 8 + 7x -2x = 89
5) 30 = 7y – 35 + 6y
Solving equations that contain fractions
5n + 7 = -3
4 4 4
4 · 5n + 7 = -3 · 4
4 4 4
5n + 7 = -3
5n + 7 – 7 = -3 – 7
5n = -10
5
5
n=-2
Multiply both side by 4 to clear fractions
Multiply both sides by 4, Multiplication Property of Equality
Subtract 7 from both sides, Subtraction Property of Equality
Divide both sides by 5, Division Property of Equality
Remember to go back an substitute for n
Solve:
1) 4 – 2p = 6
5 5 5
2) 9z + 1 = 2
4 4 4
3) x + 2 = 5
2 3 6
Solving equations with variables on both sides
is similar to solving an equation with a variable
on only one side.
You can add or subtract a term containing a variable
on both sides of an equation.
Moving terms is just like
moving a single number, you
2a + 3 = 3a
use the Properties of
Equality.
2a – 2a + 3 = 3a – 2a Subtract 2a from both sides.
3=a
Remember to keep equal (=) signs lined up to prevent errors. Always
go back and check each equation by substituting the solution into
the original equation.
Solving equations with variables on both sides.
Remember, you can move a whole
term.
4x – 7 = 5 + 7x
4x – 4x -7 = 5 + 7x -4x Subtract 4x from both sides.
-7 = 5 + 3x
-7 -5 = 5 – 5 + 3x Subtract 5 from both sides.
-12 = 3x
-12 = 3x
Divide both sides by 3.
3
3
-4 = x Remember go back and substitute for x.
Solve:
1) 5x + 2 = x + 6
2) 4y – 2 = 6y + 6
3) 4(x - 5) + 2 = x + 3
4) 4x – 5 + 2x = 13 + 9x – 21
5) 8x – 3 = 15 + 5x
Both figures have the same perimeter. What
is the perimeter.
Remember how to find
the perimeter of a
polygon?
Well, these
two
perimeters
are the
same.
Write an equation and solve the following
problem.
Sam and Ted have the same number of baseball
trading cards in their collection. Sam has 6
complete sets plus 2 individual cards, and Ted has
3 complete sets plus 20 individual cards. How
many cards are in a complete set?
Find three consecutive whole numbers such that the
sum of the first two numbers equals the third
number. Hint: Let n represent the first number.)
Solve and check.
1) 6x + 3x – x + 9 = 33
5) 5y – 2 – 8y = 31
2) -9 = 5x + 21 + 3x
6) 28 = 10a – 5a – 2
3) 4 – 2p = 6
5 5 5
7) x + 2 = 5
2 3 6
4) y – 3y + 1 = 1
2 8 4 2
8) 5n – 2 – 8n = 31