Solving Simple, Multi-Step Equations And Equations With Variables On Both Sides Worksheet Page 23
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40Writing and Solving an Equation
5 5
EXAMPLE
The circles are identical. What is the area of each circle?
16 π
64 π
○
○
○
○
2
4
A
B
C
D
x
2
The circles are identical, so the radius of each circle is the same.
4x
x + 2 = 2x
= 2x.
—
Write an equation. The radius of the purple circle is
2
− x
− x
Subtraction Property of Equality
4x
2 = x
Simplify.
Because the radius of each circle is 4, the area of each circle is
π
2
= π (4)
2
= 16 π .
r
○
So, the correct answer is
.
C
6 6
Real-Life Application
EXAMPLE
A boat travels x miles per hour upstream on the Mississippi River. On
the return trip, the boat travels 2 miles per hour faster. How far does
the boat travel upstream?
The speed of the boat on the return trip is (x + 2) miles per hour.
159
3
Red Bud
Distance upstream = Distance of return trip
=
2.5(x + 2)
3x
Write an equation.
Evansville
3x =
2.5x + 5
Distributive Property
3
− 2.5x
− 2.5x
Subtraction Property of Equality
55
0.5x = 5
Simplify.
0.5x
5
Chester
es
es
=
Ste.
—
—
Division Property of Equality
Genevieve
0.5
0.5
32
x = 10
Simplify.
The boat travels 10 miles per hour for 3 hours upstream.
So, it travels 30 miles upstream.
8.
WHAT IF?
In Example 5, the diameter of the purple circle is
3x. What is the area of each circle?
9. A boat travels x miles per hour from one island to another
island in 2.5 hours. The boat travels 5 miles per hour faster
on the return trip of 2 hours. What is the distance between
the islands?
22
Chapter 1
Equations
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