Part II: The Answers
150
Answers
1–100
60.
−
( )
3
2
5
2
,
To solve an absolute inequality of the form a b
< , where b > 0, solve the compound
inequality –b < a < b. So for the inequality 2
1 4
x − < , you have
− <
− <
− <
<
− < <
4 2
1 4
3 2
5
3
2
5
2
x
x
x
The solution set is −
( )
3
2
5
2
,
.
61.
(–∞, 1) ∪
∞
( )
9
5
,
To solve an absolute value inequality of the form a b
> , where b > 0, you have to solve
the corresponding inequalities a > b and a < –b. Therefore, for the inequality 5
7 2
x − > ,
you have to solve 5x – 7 > 2 and 5x – 7 < –2. For the first inequality, you have
5
7 2
5
9
9
5
x
x
x
− >
>
>
And for the second inequality, you have
5
7
2
5
5
1
x
x
x
− < −
<
<
Therefore, the solution set is the intervals (–∞, 1) and 9
5
, ∞
( ) .
62.
−

 

 
4
3
2
,
To solve an absolute inequality of the form a b
≤ , where b > 0, solve the compound
inequality –b ≤ a ≤ b. For the inequality − + ≤
3
1 5
x
, you have
− ≤ − + ≤
− ≤ − ≤
≥ ≥ −
5
3
1 5
6
3
4
2
4
3
x
x
x
Therefore, the solution is the interval −

 

 
4
3
2
, .
63.
7
4
The slope of a line that goes through the points (x 1 , y 1 ) and (x 2 , y 2 ) is given by m
y
y
x
x
=
−
−
2
1
2
1
.
Therefore, the slope of the line that passes through (1, 2) and (5, 9) is
m = −
−
=
9 2
5 1
7
4