Answer:
See below.
Step-by-step explanation:
It can really help to think when you see |expression| that it means the distance from expression to zero.
(a) |x| < 7 means the distance from x to 0 is less than 7. That puts x between -7 and 7. The solution set is -7 < x < 7.
(b) |x + 3| < 9 means that the distance from x + 3 to 0 is less than 9. That puts x + 3 between -9 and 9:
-9 < x + 3 < 9 Now subtract 3 from all three parts.
-12 < x < 6
(c) |y - 8| > 11 means that the distance from y - 8 to 0 is more than 11 units. That puts y - 8 in one of two places: left of -11 or right of 11.
[tex]y-8 < -11 \text{ or } y-8 > 11\\\\y < -3 \text{ or } y > 19[/tex]
(g) [tex]|3x-1| \ge 18[/tex] means that the distance from 3x - 1 to 0 is more than (or equal to) 18. Another way to say it is, 3x - 1 is farther from 0 than 18 units. That puts 3x - 1 in one of two places: to the left of -18 or to the right of 18.
[tex]3x-1 \le -18 \text{ or } 3x-1 \ge 18\\\\3x \le -17 \text{ or } 3x \ge 19\\\\x \le -\frac{17}{3} \text{ or } x \ge \frac{19}{3}[/tex]
[tex]|4y+3| \le 13[/tex] means that 4y + 3 is closer to 0 than 13; it is between -13 and 13.
[tex]-13 \le 4y+3 \le 13\\\\-16 \le 4y \le 10\\\\-4 \le y \le \frac{5}{2}[/tex]
(That last fraction is 10/4 simplified.)
