- a.
0 – .x 3
20
x (–0.3)(20) = –6
(Note: Remember to reverse the inequality
sign when dividing both sides of an inequality
by a negative number.)
- d.
–8(x+ 3) 2(–2x+ 10)
–8x– 24 –4x+ 20
–24
4 x+ 20
–44
4 x
–11 x
- b.
3(x– 16) – 29(x– 2) – 7x
3 x– 48 – 2 9 x– 18 – 7x
3 x– 50 2 x– 18
x– 50–18
x 32
- b.
–5[9 + (x– 4)] 2(13 – x)
–5[5 + x] 2(13 – x)
–25 – 5x 26 – 2x
–51 – 5x –2x
–51 3 x
–17 x
The answer can be written equivalently as
x – 17.
- a.When solving a compound inequality for
which the only expression involving the vari-
able is located between the two inequality
signs and is linear, the goal is to simplify the
inequality by adding/subtracting the constant
term in the middle portion of the inequality
to/from all three parts of the inequality, and
then to divide all three parts of the inequality
by the coefficient ofx. The caveat in the latter
step is that when the coefficient ofxis nega-
tive,both inequality signs are switched. We
proceed as follows:
–4 3 x– 1
11
–3 3 x
12
–1x≤ 4
- b.Using the same steps as in question 207,
proceed as follows:
10
3(4 – 2x) –2 70
10
( 12 – 6x– 2 70
10
10 – 6x 70
0
– 6x 60
0 x–10
The last compound inequality above can be
written equivalently as –10x 0.
Set 14 (Page 24)
- c.Using the fact that |a| =bif and only ifa=b,
we see that solving the equation |–x| – 8 = 0, or
equivalently |–x| = 8, is equivalent to solving –x
=8. We solve these two equations separately:
- x= 8 –x= –8
x= –8 x= 8
So, both –8 and 8 are solutions of this equation.
- a.We rewrite the given equation as an equiva-
lent one solved for |x|, as follows:
2|x| + 4 = 0
2|x| = –4
|x| = –2
The left side must be nonnegative for any
value ofx(since it is the absolute value of an
expression), and the right side is negative, so
there can be no solution to this equation.
ANSWERS & EXPLANATIONS–
