Geo_Book_Answers

Answers to Exercises
USING YOUR ALGEBRA SKILLS 4
1. false 2. true
3. not a solution 4. solution
5. not a solution 6. x 7
7. y 4 8. x 8
9. x 4.2 10. n 1
2
11. x 2 12. t 18
13. n 2
5 14a. x 9
4
9
14b. x ; 4 The two methods produce identical
results. Multiplying by the lowest common
denominator (which is comprised of the factors of
both denominators) and then reducing common
factors (which clears the denominators on either
side) is the same as simply multiplying each numerator
by the opposite denominator (or cross multiplying).
Algebraically you could show that the two methods
are equivalent as follows:
a c
b
d
bda b bd c d
abd
b
bcd
d
ad bc
The method of “clearing fractions” results in the
method of “cross multiplying.”
50 ANSWERS TO EXERCISES
15. You get an equation that is always false, so
there is no solution to the equation.
16. Camella is not correct. Because the equation
0 0 is always true, the truth of the equation does
not depend on the value of x. Therefore, x can be
any real number. Camella’s answer, x 0, is only
one of infinitely many solutions.
17.
x
2x
2x
If x equals the measure of the vertex angle, then
the base angles each measure 2x. Applying the
Triangle Sum Conjecture results in the following
equation:
x 2x 2x 180°
5x 180°
x 36°
The measure of the vertex angle is 36° and the
measure of each base angle is 72°.