1
What is the distance between 33 and -73 on the number line?
Medium
ExplanationThe distance between two points on a number line is |33 − (-73)| = 106.
2
Among -54, 87, 44, and -30, which is closest to 0 on the number line?
Medium
ExplanationThe number closest to 0 has the smallest absolute value. |-30| = 30, which is the smallest among the options.
3
Among -51, -89, -88, and -47, which is closest to 0 on the number line?
Medium
ExplanationThe number closest to 0 has the smallest absolute value. |-47| = 47, which is the smallest among the options.
4
Which is greater: |-72| or |23|?
Medium
Explanation|-72| = 72 and |23| = 23, so |-72| is greater.
5
What is the solution set of |x − 35| > 20?
Medium
Explanation|x − 35| > 20 means x is farther than 20 from 35, giving x < 15 or x > 55.
6
How many integers satisfy |x + 8| < 3?
Medium
Explanation|x + 8| < 3 means -11 < x < -5. The integers strictly between -11 and -5 number 5.
Explanation|44 ÷ 11| = |44| ÷ |11| = 44 ÷ 11 = 4.
8
What are the solutions to |x| + 18 = 29?
Medium
Explanation|x| + 18 = 29 means |x| = 11, so x = 11 or x = -11.
9
For a = 24 and b = 25, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
Explanation|a + b| = 49 and |a| + |b| = 49. Since a and b have the same sign, the two are equal.
10
Which is farther from -22 on the number line: -2 or -38?
Medium
ExplanationDistance from -22: |-2 − (-22)| = 20, and |-38 − (-22)| = 16. So -2 is farther.
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11
Which is farther from -17 on the number line: -17 or -62?
Medium
ExplanationDistance from -17: |-17 − (-17)| = 0, and |-62 − (-17)| = 45. So -62 is farther.
ExplanationAbsolute value gives the distance from 0, which is always non-negative, so |-26| = 26.
13
Among -40, 25, 12, and -33, which is closest to 0 on the number line?
Medium
ExplanationThe number closest to 0 has the smallest absolute value. |12| = 12, which is the smallest among the options.
14
Among -45, -33, 18, and -68, which is closest to 0 on the number line?
Medium
ExplanationThe number closest to 0 has the smallest absolute value. |18| = 18, which is the smallest among the options.
15
What is the distance between -76 and -5 on the number line?
Medium
ExplanationThe distance between two points on a number line is |-76 − (-5)| = 71.
16
For a = 23 and b = -23, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
Explanation|a + b| = 0 and |a| + |b| = 46. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
17
What is the midpoint between -13 and 41 on the number line?
Medium
ExplanationThe midpoint of -13 and 41 is (-13 + 41) / 2 = 28/2 = 14.
18
How many integers satisfy |x + 24| < 19?
Medium
Explanation|x + 24| < 19 means -43 < x < -5. The integers strictly between -43 and -5 number 37.
19
What are the solutions to |9x + 9| = 99?
Medium
Explanation9x + 9 = 99 or 9x + 9 = −99, which solve to x = 10 and x = -12.
20
Which of the following numbers lies between -36 and -19?
Medium
Explanation-27 lies strictly between -36 and -19, while the other options fall outside that range.
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21
Which is farther from 4 on the number line: 2 or 31?
Medium
ExplanationDistance from 4: |2 − 4| = 2, and |31 − 4| = 27. So 31 is farther.
22
For a = 3 and b = -6, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
Explanation|a + b| = 3 and |a| + |b| = 9. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
23
What are the solutions to |x| + 15 = 28?
Medium
Explanation|x| + 15 = 28 means |x| = 13, so x = 13 or x = -13.
24
What is the solution set of |x + 28| < 18?
Medium
Explanation|x + 28| < 18 means x is within 18 of -28, giving -46 < x < -10.
Explanation|-4 ÷ -4| = |-4| ÷ |-4| = 4 ÷ 4 = 1.
26
What is the midpoint between 45 and -8 on the number line?
Medium
ExplanationThe midpoint of 45 and -8 is (45 + -8) / 2 = 37/2 = 37/2.
27
What are the solutions to |x| + 11 = 29?
Medium
Explanation|x| + 11 = 29 means |x| = 18, so x = 18 or x = -18.
28
Which is farther from 7 on the number line: -8 or -45?
Medium
ExplanationDistance from 7: |-8 − 7| = 15, and |-45 − 7| = 52. So -45 is farther.
29
If |x| = |-35|, what are the possible values of x?
Medium
Explanation|x| = |-35| = 35 means x is 35 units from 0, so x = 35 or x = -35.
30
How many solutions does the equation |x − 28| = 27 have?
Medium
Explanation|x − 28| = 27: since 27 is positive, there are two solutions.
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31
How many solutions does |x + 31| = −24 have?
Medium
ExplanationAn absolute value can never equal a negative number, so |x + 31| = −24 has no solution.
32
What is the length of the solution interval for |x − 18| < 23?
Medium
Explanation|x − 18| < 23 describes the interval (-5, 41), which has length 41 − (-5) = 46.
33
What is the distance between -91 and 39 on the number line?
Medium
ExplanationThe distance between two points on a number line is |-91 − 39| = 130.
34
What are the solutions to |x| + 25 = 37?
Medium
Explanation|x| + 25 = 37 means |x| = 12, so x = 12 or x = -12.
Explanation|-7 × -17| = |-7| × |-17| = 7 × 17 = 119.
36
What is the midpoint between -56 and 4 on the number line?
Medium
ExplanationThe midpoint of -56 and 4 is (-56 + 4) / 2 = -52/2 = -26.
37
For a = -29 and b = 16, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
Explanation|a + b| = 13 and |a| + |b| = 45. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
38
What is the midpoint between 25 and -43 on the number line?
Medium
ExplanationThe midpoint of 25 and -43 is (25 + -43) / 2 = -18/2 = -9.
39
What is the midpoint between -56 and 19 on the number line?
Medium
ExplanationThe midpoint of -56 and 19 is (-56 + 19) / 2 = -37/2 = -37/2.
40
Which is farther from 27 on the number line: -9 or -57?
Medium
ExplanationDistance from 27: |-9 − 27| = 36, and |-57 − 27| = 84. So -57 is farther.
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41
How many solutions does |x − 17| = −11 have?
Medium
ExplanationAn absolute value can never equal a negative number, so |x − 17| = −11 has no solution.
42
What is the solution set of |x + 36| > 14?
Medium
Explanation|x + 36| > 14 means x is farther than 14 from -36, giving x < -50 or x > -22.
43
Which is farther from -26 on the number line: 80 or -62?
Medium
ExplanationDistance from -26: |80 − (-26)| = 106, and |-62 − (-26)| = 36. So 80 is farther.
44
How many solutions does the equation |x − 8| = 22 have?
Medium
Explanation|x − 8| = 22: since 22 is positive, there are two solutions.
45
What is the solution set of |x + 34| > 26?
Medium
Explanation|x + 34| > 26 means x is farther than 26 from -34, giving x < -60 or x > -8.
46
How many solutions does |x + 13| = −11 have?
Medium
ExplanationAn absolute value can never equal a negative number, so |x + 13| = −11 has no solution.
47
Which is greater: |53| or |75|?
Medium
Explanation|53| = 53 and |75| = 75, so |75| is greater.
48
What is the solution set of |x − 40| > 8?
Medium
Explanation|x − 40| > 8 means x is farther than 8 from 40, giving x < 32 or x > 48.
49
What is the solution set of |x − 19| < 1?
Medium
Explanation|x − 19| < 1 means x is within 1 of 19, giving 18 < x < 20.
50
How many solutions does |x − 40| = −14 have?
Medium
ExplanationAn absolute value can never equal a negative number, so |x − 40| = −14 has no solution.
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51
For a = -27 and b = -26, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
Explanation|a + b| = 53 and |a| + |b| = 53. Since a and b have the same sign, the two are equal.
52
What is the midpoint between 55 and 27 on the number line?
Medium
ExplanationThe midpoint of 55 and 27 is (55 + 27) / 2 = 82/2 = 41.
53
For a = 3 and b = -12, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
Explanation|a + b| = 9 and |a| + |b| = 15. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
54
What is the distance between -94 and -27 on the number line?
Medium
ExplanationThe distance between two points on a number line is |-94 − (-27)| = 67.
Explanation|14 ÷ 14| = |14| ÷ |14| = 14 ÷ 14 = 1.
Explanation|14 × -3| = |14| × |-3| = 14 × 3 = 42.
57
Among 25, -69, -67, and 86, which is closest to 0 on the number line?
Medium
ExplanationThe number closest to 0 has the smallest absolute value. |25| = 25, which is the smallest among the options.
58
What are the solutions to |7x − 42| = 35?
Medium
Explanation7x − 42 = 35 or 7x − 42 = −35, which solve to x = 11 and x = 1.
59
For a = 18 and b = 20, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
Explanation|a + b| = 38 and |a| + |b| = 38. Since a and b have the same sign, the two are equal.
60
What is the distance between 77 and -43 on the number line?
Medium
ExplanationThe distance between two points on a number line is |77 − (-43)| = 120.
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61
What is the distance between 18 and 65 on the number line?
Medium
ExplanationThe distance between two points on a number line is |18 − 65| = 47.
62
Which is farther from 15 on the number line: -53 or -31?
Medium
ExplanationDistance from 15: |-53 − 15| = 68, and |-31 − 15| = 46. So -53 is farther.
63
How many integers satisfy |x + 2| < 10?
Medium
Explanation|x + 2| < 10 means -12 < x < 8. The integers strictly between -12 and 8 number 19.
64
What is the midpoint between -48 and -29 on the number line?
Medium
ExplanationThe midpoint of -48 and -29 is (-48 + -29) / 2 = -77/2 = -77/2.
65
Which is farther from -19 on the number line: 69 or 3?
Medium
ExplanationDistance from -19: |69 − (-19)| = 88, and |3 − (-19)| = 22. So 69 is farther.
66
What is the length of the solution interval for |x − 6| < 17?
Medium
Explanation|x − 6| < 17 describes the interval (-11, 23), which has length 23 − (-11) = 34.
67
What are the solutions to |x| + 25 = 47?
Medium
Explanation|x| + 25 = 47 means |x| = 22, so x = 22 or x = -22.
68
What is the distance between -91 and -39 on the number line?
Medium
ExplanationThe distance between two points on a number line is |-91 − (-39)| = 52.
69
Which is farther from 5 on the number line: 29 or -24?
Medium
ExplanationDistance from 5: |29 − 5| = 24, and |-24 − 5| = 29. So -24 is farther.
70
What are the solutions to |x − 31| = 19?
Medium
Explanation|x − 31| = 19 means x is 19 away from 31, so x = 31 + 19 = 50 or x = 31 − 19 = 12.
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71
How many solutions does |x + 18| = −27 have?
Medium
ExplanationAn absolute value can never equal a negative number, so |x + 18| = −27 has no solution.
72
What is the distance between 71 and 93 on the number line?
Medium
ExplanationThe distance between two points on a number line is |71 − 93| = 22.
73
What are the solutions to |x + 38| = 5?
Medium
Explanation|x + 38| = 5 means x is 5 away from -38, so x = -38 + 5 = -33 or x = -38 − 5 = -43.
74
If |x| = |-5|, what are the possible values of x?
Medium
Explanation|x| = |-5| = 5 means x is 5 units from 0, so x = 5 or x = -5.
75
What is the solution set of |x + 10| < 6?
Medium
Explanation|x + 10| < 6 means x is within 6 of -10, giving -16 < x < -4.
Explanation|-117 ÷ 13| = |-117| ÷ |13| = 117 ÷ 13 = 9.
77
Which is greater: |-3| or |-46|?
Medium
Explanation|-3| = 3 and |-46| = 46, so |-46| is greater.
78
Which of the following numbers lies between -30 and -13?
Medium
Explanation-23 lies strictly between -30 and -13, while the other options fall outside that range.
79
How many solutions does |x − 5| = −5 have?
Medium
ExplanationAn absolute value can never equal a negative number, so |x − 5| = −5 has no solution.
80
How many solutions does |x − 22| = −14 have?
Medium
ExplanationAn absolute value can never equal a negative number, so |x − 22| = −14 has no solution.
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81
Which is greater: |-21| or |2|?
Medium
Explanation|-21| = 21 and |2| = 2, so |-21| is greater.
82
What is the solution set of |x + 20| < 8?
Medium
Explanation|x + 20| < 8 means x is within 8 of -20, giving -28 < x < -12.
83
How many solutions does |x + 2| = −11 have?
Medium
ExplanationAn absolute value can never equal a negative number, so |x + 2| = −11 has no solution.
84
What are the solutions to |x| + 3 = 34?
Medium
Explanation|x| + 3 = 34 means |x| = 31, so x = 31 or x = -31.
85
What are the solutions to |x − 39| = 18?
Medium
Explanation|x − 39| = 18 means x is 18 away from 39, so x = 39 + 18 = 57 or x = 39 − 18 = 21.
86
What is the distance between -35 and 97 on the number line?
Medium
ExplanationThe distance between two points on a number line is |-35 − 97| = 132.
87
Which is farther from 13 on the number line: -56 or -22?
Medium
ExplanationDistance from 13: |-56 − 13| = 69, and |-22 − 13| = 35. So -56 is farther.
88
Among 26, -18, -58, and -50, which is closest to 0 on the number line?
Medium
ExplanationThe number closest to 0 has the smallest absolute value. |-18| = 18, which is the smallest among the options.
Explanation|14 × -7| = |14| × |-7| = 14 × 7 = 98.
90
What is the solution set of |x − 21| > 3?
Medium
Explanation|x − 21| > 3 means x is farther than 3 from 21, giving x < 18 or x > 24.
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91
Among -3, 24, -70, and 86, which is closest to 0 on the number line?
Medium
ExplanationThe number closest to 0 has the smallest absolute value. |-3| = 3, which is the smallest among the options.
92
What is the length of the solution interval for |x + 35| < 15?
Medium
Explanation|x + 35| < 15 describes the interval (-50, -20), which has length -20 − (-50) = 30.
93
For a = 12 and b = -25, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
Explanation|a + b| = 13 and |a| + |b| = 37. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
94
What are the solutions to |x + 25| = 23?
Medium
Explanation|x + 25| = 23 means x is 23 away from -25, so x = -25 + 23 = -2 or x = -25 − 23 = -48.
Explanation|48 ÷ -6| = |48| ÷ |-6| = 48 ÷ 6 = 8.
96
Which is farther from 2 on the number line: 25 or 72?
Medium
ExplanationDistance from 2: |25 − 2| = 23, and |72 − 2| = 70. So 72 is farther.
Explanation|31| − |4| = 31 − 4 = 27. (Note this is generally different from |31 − 4|.)
98
For a = 22 and b = 15, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
Explanation|a + b| = 37 and |a| + |b| = 37. Since a and b have the same sign, the two are equal.
99
Which is greater: |-17| or |40|?
Medium
Explanation|-17| = 17 and |40| = 40, so |40| is greater.
100
Among -68, 39, 51, and 53, which is closest to 0 on the number line?
Medium
ExplanationThe number closest to 0 has the smallest absolute value. |39| = 39, which is the smallest among the options.