326 MCGRAW-HILL’S SAT
- 7 20 − 2 n> 5
Subtract 20: − 2 n> − 15
Divide by −2: n< 7.5 (Don’t forget the switch!)
The greatest integer ncould be, then, is 7. Notice that
7 also satisfies the other inequality: 2(7)/3 =4.666,
which of course is greater than 4.
9.C Plugging in isn’t good enough here, because
more than one expression may be correct. The
best method is substitution, using b= 2 a−4 and
c=a+2:
I. b−c+ 6 =(2a−4) −(a+2) + 6 =a(Yes!)II.
(Yes!)
III. 2c−b− 8 =2(a+2) −(2a−4) − 8 = 0
(No.)bc aa a
a++
=
()− ++()+
==
2
3
24 22
3
3
3
10.D The distance from 1 to xis ⏐x− 1 ⏐and the dis-
tance from 3 to xis ⏐x− 3 ⏐, so I is clearly correct.
To see why III is true, notice that 2 is the only num-
ber equidistant from 1 and 3, so all numbers that
are farther from 1 than from 3 are greater than 2.