Algebraic Manipulation Worksheets With Answers - Craven Community College Page 14
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297. A – 4
8.
3
+
1
A
X + 3
X – 1
A + 4
1
+
2
A
X – 1
X + 2
Solve each of the following equations.
9.
4
= 2
10.
5
+
7
=
21
2
2
2
X + 3
X
X
+ X – 12
X
+ 7X + 12
4X
– 36
11. The speed of the current in a river is 5mph. If a boat can travel 198 miles with the current in the same
time it could travel 138 miles against the current, what is the speed of the boat in still water?
12. An inlet pipe can fill a tank in 10 minutes. A drain can empty the tank in 12 minutes. If the tank is
empty and both the pipe and the drain are open, how long will it take before the tank overflows?
13. Connie can type 600 words in 5 minutes less than it takes Katie to type 600 words. If Connie can
type at a rate of 20 words per minute faster than Katie types, find Connie’s typing rate.
14. The ratio of the squares to two consecutive even integers is 9/16. Find these integers.
R
R
OOTS AND
ADICALS
Simplifying Radical Expressions
Radical expressions are algebraic expressions which contain a radical. A radical expression is simplified
when the radicand (expression under the radical) does not contain any powers greater than or equal to the
index, there are no radicals in the denominator and all fractions are in the lowest terms.
V
5
8
Example:
162X
Y
V
4
8
81 • 2X
XY
Write factors as perfect squares if possible
2
4
V
9X
Y
2X
Remove the squares
Adding and Subtracting Radical Expressions
Adding and Subtracting can be done on terms with like radical portions. When the terms have like racial
parts, add or subtract in the same manner as when adding or subtracting like terms.
V
V
–
V
Example:
45 +
125
75
14
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