Victory for the ACT Student Text 15e

456 • C AMBRIDGE P RACTICE T EST R EINFORCEMENT And: ( ) x − − = − + = = = Double-check each possible value for x x 5 2 7 x x x 5 2 7 5 2 7 6 2 12

in the original equation:

( ) 5 2 1 7 − = − − = + = = 5 2 7 7 7

9

And:

x 5 2 7 − =

( ) 5 2 6 7 = − = − = 9 Therefore, the solution set is { 1 ǡ ͸ȔǤ Alternatively, check the answer choice values by plugging them into the equation, starting with (F). 21. (D) (p. 382) Mathematics/Algebra and Functions/Manipulating Algebraic Expressions/Basic Algebraic Manipulations . To combine the fractions in the numerator, rewrite them using the lowest common denominator, which is x : 3 3 3 5 12 7 7 7 −

x x

x c c m m 1 −

−

3

x

=

−

−

( x x

( x x

1

)

1

)

( x x x x

3 3

−

x

=

−

1

)

−

x

( 3 1

)

x

=

−

( x x

1

)

−

x

1

3

( 3 1

)

=

=

:

x

−

( x x

x

2

1

)

•‡ –Š‡ ‡“—ƒ–‹‘ ˆ‘” ϐ‹†‹‰

the slope of a line, where m 2 1

is the slope and ( , ) x y 1 1

and ( , ) x y 2 2

are the two given points:

22. (K) (p. 383) Mathematics/Algebra and Functions/Coordinate Geometry/Slope of a Line .

x x y y − −

=

m

2 1

4 3 7 5 − − −

=

( )

2

=

7