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Zorluk: OrtaIntegers, Absolute Value, and Number Lines

On a standard number line, point mm is located at coordinate −9-9, and point nn is located to the right of point mm. If the distance between point mm and point nn is given by the expression ∣3k−6∣|3k - 6| where k=−4k = -4, what is the coordinate of point nn?

  1. A
    −27-27
  2. B
    −15-15
  3. C
    −3-3
  4. 99Cevap
  5. E
    2727

Cevap

The coordinate of point nn is 99.
First, evaluate the distance expression ∣3k−6∣|3k - 6| when k=−4k = -4: 3(−4)−6=−183(-4) - 6 = -18, and ∣−18∣=18|-18| = 18. Since point nn is located to the right of point mm (which is at −9-9), add the distance of 1818 to −9-9: −9+18=9-9 + 18 = 9. Thus, the coordinate of point nn is 99.

Adım Adım Çözüm

1
Evaluate the expression inside the absolute value for k=−4k = -4
3(−4)−6=−12−6=−183(-4) - 6 = -12 - 6 = -18
Substitute k=−4k = -4 into 3k−63k - 6 following the order of operations.
2
Calculate the absolute value to find the distance
∣−18∣=18|-18| = 18
Distance is non-negative, so taking the absolute value yields a distance of 18 units.
3
Find the position of point nn relative to point mm
n=−9+18=9n = -9 + 18 = 9
Since point nn lies to the right of point m=−9m = -9 on the number line, add the distance of 18 units to −9-9.

Anahtar Kavram

Distance on a Number Line using Absolute Value
Tahmini Süre:1m 0s
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Konular

Integers, Absolute Value, and Number Lines

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