3-8 Solving Equations and Formulas - Mona Shores Blogs

3-8 Solving
Equations and
Formulas
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Objectives
• Students will solve equations for given
variables.
• Students will use formulas to solve
real-world problems.
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Solve for Variables
• Some equations contain more than one
variable. You may need to solve for
one of the variables. Solving for a
variable means getting the variable by
itself on one side of the equation.
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Solve for Variables
• Solve for x: y = 4x + 8
y = 4x + 8
-8 - 8
Y – 8 = 4x
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Solve for Variables
• Solve for x: y = 4x + 8
y = 4x + 8
-8 - 8
Y – 8 = 4x
4 4
1/4y – 2 = x
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Example 1
Solve 5b + 12c = 9 for b
5b + 12c = 9
-12c - 12c
5b = 9 – 12c
5 5
9 −12c
b =
5
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Example 2
Solve 7x – 2z = 4 – xy for x
7x – 2z = 4 – xy
+2z + 2z
7x = 4 – xy + 2z
+xy +xy
7x + xy = 4 + 2z
x(7+y) = 4 + 2z
(7+y) (7+y)
x
4 + 2z
= 7 + y
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Practice
• 2w – y = 7w –2, for w
• ab + 3c = 2d
• 2/5h + g = d for h
• 9s – 5g = -4u, for s
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Example 3
A car’s fuel economy E (miles per gallon) is
m
given by the formula E = , where m is the
g
number of miles driven and g is the number
of gallons of fuel used. Solve for m.
m = Eg
If Claudia’s car has an average fuel
consumption of 30 miles per gallon and she
used 9.5 gallons, how far did she drive
m = 30•9.5
m = 285 mi
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Example 4
The formula for the volume of a cylinder is
V=πr 2 h, where r is the radius of the
cylinder and h is the height. Solve for h.
V
h =
πr
2
What is the height of a cylindrical
swimming pool that has a radius of 12
feet and a volume of 1810 cubic feet
about 4 ft
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