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Zorluk: KolayReal Numbers, Number Line, and Absolute Value

On the real number line, the point PP corresponds to the real number xx. If ∣x−3∣=7|x - 3| = 7, which of the following is a possible value of x+5x + 5?

  1. A
    −9-9
  2. B
    −4-4
  3. 11Cevap
  4. D
    99
  5. E
    1212

Cevap

The correct answer is 11.
Solving ∣x−3∣=7|x - 3| = 7 produces two possible values for xx: x=10x = 10 and x=−4x = -4. Substituting x=−4x = -4 into x+5x + 5 yields −4+5=1-4 + 5 = 1, which is listed among the choices.

Adım Adım Çözüm

1
Set up the two linear equations defined by the absolute value equation ∣x−3∣=7|x - 3| = 7.
The two cases are x−3=7x - 3 = 7 and x−3=−7x - 3 = -7.
By definition of absolute value, ∣k∣=7|k| = 7 means k=7k = 7 or k=−7k = -7.
2
Solve each case for xx.
From x−3=7x - 3 = 7, x=10x = 10. From x−3=−7x - 3 = -7, x=−4x = -4.
Adding 33 to both sides of each equation isolates xx.
3
Evaluate x+5x + 5 for both solutions of xx.
If x=10x = 10, x+5=15x + 5 = 15. If x=−4x = -4, x+5=1x + 5 = 1.
Substitute each possible value of xx into the expression x+5x + 5.

Anahtar Kavram

Absolute Value as Distance on the Number Line
Tahmini Süre:45s
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