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Zorluk: KolayLinear Equations in One and Two Variables

If ∣2x−3∣=7|2x - 3| = 7, which of the following is a possible value of xx?

  1. 55Cevap
  2. B
    −5-5
  3. C
    22
  4. D
    1010
  5. E
    −4-4

Cevap

The value 55 is a valid solution to the given absolute value equation.
The absolute value equation ∣2x−3∣=7|2x - 3| = 7 splits into two linear equations: 2x−3=72x - 3 = 7 and 2x−3=−72x - 3 = -7. Solving the first equation gives 2x=102x = 10, so x=5x = 5. Solving the second gives 2x=−42x = -4, so x=−2x = -2. Among the listed options, 55 is the correct solution.

Adım Adım Çözüm

1
Set up the two cases for the absolute value equation ∣2x−3∣=7|2x - 3| = 7.
Case 1: 2x−3=72x - 3 = 7; Case 2: 2x−3=−72x - 3 = -7.
An absolute value expression ∣u∣=c|u| = c (where c≥0c \geq 0) resolves to u=cu = c or u=−cu = -c.
2
Solve Case 1: 2x−3=72x - 3 = 7.
2x=10  ⟹  x=52x = 10 \implies x = 5.
Add 3 to both sides and divide by 2.
3
Solve Case 2: 2x−3=−72x - 3 = -7.
2x=−4  ⟹  x=−22x = -4 \implies x = -2.
Add 3 to both sides and divide by 2.
4
Compare the solutions (x=5x = 5 and x=−2x = -2) with the given choices.
The value 55 is present among the options.
Identifies the correct choice matching one of the calculated solutions.

Anahtar Kavram

Solving Linear Absolute Value Equations
Tahmini Süre:45s
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Konular

Linear Equations in One and Two Variables

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