CHAPTER 8 / ESSENTIAL ALGEBRA I SKILLS 325
Concept Review 6
1.⏐y− 3 ⏐< 52.⏐a− 2 ⏐= ⏐b+ 2 ⏐
3.⏐x+ 1 ⏐≤ 10
4.⏐a−b⏐≤ 2 ⏐a−c⏐
5.⏐x− 3 ⏐< 2- y^2 ≥^4
Take the square root: ⏐y⏐≥ 2
Interpret without absolute value: y≤−2 or y≥ 2
Graph: - 6 x> 2x^2
Divide by xwith conditions: if x> 0, then 6 > 2x
if x< 0, then 6 < 2x
Simplify: if x> 0, then 3 > x,so 0 < x< 3
if x< 0, then 3 < x(no solution)
Graph: - − 3 x≥ 12
Divide by −3: x≤− 4
Graph:
9. 5 −x^2 < 5
Subtract 5: −x^2 < 0
Multiply by −1 (and “switch”): x^2 > 0
Take the square root: ⏐x⏐> 0
Interpret: x> 0 or x< 0
Graph: - x+3 < x− 1
Subtract x: 3 < − 1
But this is impossible, so there’s no solution! - (D) If you plug in a=4, then b=1 and c=−2. Since
you’re looking for an expression that equals a,plug
these into the choices and see which one gives a=4:
(A) 3(1) +(−2) − 1 = 0
(B) 3(1) −(−2) + 1 = 6
(C) (7(1) −(−2) +1)/2 = 5
(D) (7(1) −(−2) −1)/2 = 4
(E) (7(1) +(−2) −1)/2 = 2
Since (D) is the only choice that gives 4, it is the
right choice. To solve it algebraically, solve each
equation for a:
a= 2 b−c
a= 5 b− 1
Add the equations: 2 a= 7 b−c− 1
Divide by 2: a=(7b−c−1)/2
Answer Key 6:
Inequalities, Absolute Values, and Plugging In
SAT Practice 6
1.A 2 −4(−5) = 2 + 20 =22, which is not less
than 20.
2.C To satisfy the inequalities, xmust be negative,
ymust be negative, and zmust be positive. You
might choose x=−1, y=−1, and z=1 to confirm
that (C) is the only one that gives a positive value.
3.C ⏐x− 2 ⏐< 1
Translate without absolute value: −1 < x−2 < 1
Add 2: 1 < x< 3
4.E All absolute values are greater than or equal
to zero, so any value of mwould satisfy ⏐m⏐> −2.
5.B You can solve by plugging in for the unknowns,
but be careful to choose values that work in the equa-
tion. The simplest values that work are r=35, w=7, and
a=5. In this case, r−w= 35 − 7 =28. If you plug a= 5
into the choices, (B) is the only one that equals 28.Or you can solve algebraically by expressing randwin terms of a. r= 7 aand so.
6.C You might plug in k=2. Since xis the aver-
age of kand 10, x=(2 +10)/2 =6. Since yis the
average of kand 4, y=(2 +4)/2 =3. The average
of xand y,then, is (6 +3)/2 =4.5. If you then plug
k=2 into the choices, (C) is the only choice that
equals 4.5.
7.B Plug in x=3. Then m=2(3) − 5 =1 and n=(3)
+ 7 =10. The question asks for an expression that
equals x,so look for 3 in the choices when you
plugin m=1 and n=10. The only choice that
gives you 3 is (B).rwaa aa
a
−=−= −= 77
5
35
5
7
5
28
5
wa=