Question

real - number operations with absolute value
-|5 - 11|=-|-6|=-6 |-4|+|-3|=4 + 3 = 7
the absolute value of a number is its distance from zero.
for example: |5| = 5 |-6| = 6 |0| = 0
simplify.

1. |-3|=
2. |-14|=
3. 9+|-4|=
4. -5|4|+|5|=
5. |4|-|7|=
6. |21|+9=
7. 23+|8|=
8. |12|-|-15|=
9. 7-|-23|+|-7|=
10. |-6|+|8|=
11. -|-3 + 7|=
12. -|-5 + 10|=
13. |-9|+|23|=
14. |-17|-|-17|=
15. |1|-|0|+6=
16. |-67|-|-17|=
17. |4|-|-12|-4=
18. |3 - 13|=
19. |23|-|-12|=
20. |9|+|-9|=

Explanation:

Step1: Recall absolute - value definition

The absolute value of a number \(a\), denoted as \(|a|\), is the non - negative value of \(a\) (its distance from zero). For example, if \(a\geq0\), then \(|a| = a\); if \(a<0\), then \(|a|=-a\).

Step2: Solve each problem one by one

1. For \(|-3|\), since \(-3<0\), \(|-3| = 3\).
2. For \(|-14|\), since \(-14<0\), \(|-14| = 14\).
3. First, find \(|-4| = 4\), then \(9+|-4|=9 + 4=13\).
4. First, \(|4| = 4\) and \(|5| = 5\), then \(-5|4|+|5|=-5\times4 + 5=-20 + 5=-15\).
5. \(|4| = 4\) and \(|7| = 7\), so \(|4|-|7|=4 - 7=-3\).
6. \(|21| = 21\), then \(|21|+9=21 + 9=30\).
7. \(|8| = 8\), so \(23+|8|=23 + 8=31\).
8. \(|12| = 12\) and \(|-15| = 15\), then \(|12|-|-15|=12 - 15=-3\).
9. \(|-23| = 23\) and \(|-7| = 7\), then \(7-|-23|+|-7|=7-23 + 7=-9\).
10. \(|-6| = 6\) and \(|8| = 8\), then \(|-6|+|8|=6 + 8=14\).
11. First, \(-3 + 7 = 4\), then \(-|-3 + 7|=-|4|=-4\).
12. First, \(-5 + 10 = 5\), then \(-|-5 + 10|=-|5|=-5\).
13. \(|-9| = 9\) and \(|23| = 23\), then \(|-9|+|23|=9 + 23=32\).
14. \(|-17| = 17\), then \(|-17|-|-17|=17-17 = 0\).
15. \(|1| = 1\) and \(|0| = 0\), then \(|1|-|0|+6=1-0 + 6=7\).
16. \(|-67| = 67\) and \(|-17| = 17\), then \(|-67|-|-17|=67-17 = 50\).
17. \(|4| = 4\) and \(|-12| = 12\), then \(|4|-|-12|-4=4-12 - 4=-12\).
18. First, \(3-13=-10\), then \(|3 - 13|=|-10| = 10\).
19. \(|23| = 23\) and \(|-12| = 12\), then \(|23|-|-12|=23-12 = 11\).
20. \(|9| = 9\) and \(|-9| = 9\), then \(|9|+|-9|=9 + 9=18\).

Answer:

1. 3
2. 14
3. 13
4. -15
5. -3
6. 30
7. 31
8. -3
9. -9
10. 14
11. -4
12. -5
13. 32
14. 0
15. 7
16. 50
17. -12
18. 10
19. 11
20. 18