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Review of Solving Equations: The Final Challenge
Ex. 1) 5
8
3
2x The goal is to get 1x
alone.
To do this, multiply
both sides by ,
which is the reciprocal
of .
2
3
3
2
2
3
5
8
3
2
2
3x
Reduce fractions if possible.
4
1
Multiply fractions, and simplify.5
22
5
121 x
Ex. 2) 22
15 x Subtract 5 from both sides
to get the x term alone.
5 5
1
2-
1
2-
141
14x
1
7
2
1
x Multiply both sides by ,
which is the reciprocal of .
1
2
2
1
Reduce fractions if possible.
Multiply fractions, and simplify.
Ex. 3) 15465 x
Add 4 to both sides to get 1x alone.4 4
To eliminate the fraction,
multiply both sides by ,
which is the reciprocal of .
5
6
6
5
56
115
65
56 4x
Reduce fractions if possible.
-3
1
184 x
14x
Ex. 4) The perimeter of Mr. Mac Gregor’s garden is 64 meters. The length of the garden in 20 meters. What is the width of the garden? Write and solve an equation to answer this question!
Let w = width of the rectangle
The perimeter is the distance around the outside of the rectangle.
P = 2(Length) + 2(width)P = 2L + 2w
- 40 -4024 = 2w
2 2
12 m = w The width of the garden is 12 meters.
20 m
20 m
w w
64 = 2(20) + 2w64 = 40 + 2w
Ex. 5) Students at the rec center are taking a trip to the county fair. The cost of the trip is $52 per student. This price includes a concert ticket worth $11 and 2 passes for the rides and the game booths. If the passes are worth the same amount of money, how much does 1 pass cost? Write and solve an equation to answer this question!
Let x = cost of 1 pass
Total cost = cost of concert ticket + cost of 2 passes
- 11 -11
41 = 2x2 2
$20.50 = x One pass would cost $20.50.
52 = 11 + 2x
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