College Algebra 9th txtbk

SECTION 1–1 Linear Equations and Applications 49
15 p 15 a p 3 p 5 7b
*
15p 15 p 3 15 p 5 15 7
15p 5p 3p 105
15p 8p 105
7p 105
p 15
The perimeter is 15 meters.
Combine like terms.
Subtract 8p from both sides.
Divide both sides by 7.
p
3 15
3 5
CHECK Side 1
p Side 2
5 15
5 3
7 Side 3
15 meters Perimeter
MATCHED PROBLEM 4
If one side of a triangle is one-fourth the perimeter, the second side is 7 centimeters, and
the third side is two-fifths the perimeter, what is the perimeter?
ZZZ CAUTION ZZZ
A very common error occurs about now—students tend to confuse algebraic expressions
involving fractions with algebraic equations involving fractions.
Consider these two problems:
x
x
(A) Solve:
(B) Add:
2 x 2 x 3 10 3 10
The problems look very much alike but are actually very different. To solve the equation
in (A) we multiply both sides by 6 (the LCD) to clear the fractions. This works
so well for equations that students want to do the same thing for problems like (B).
The only catch is that (B) is not an equation, and the multiplication property of equality
does not apply. If we multiply (B) by 6, we simply obtain an expression 6 times
as large as the original! Compare these correct solutions:
x
(A)
2 x 3 10 x
(B)
2 x 3 10
6 x 2 6 x 3 6 10
3x 2x 60
5x 60
x 12
3 x
3 2 2 x
2 3 6 10
6 1
3x
6 2x
6 60
6
5x 60
6
*Throughout the book, dashed boxes—called think boxes—are used to represent steps that may be performed
mentally.