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Zorluk: KolayInequalities and Absolute Value Equations

If ∣3x+4∣=19|3x + 4| = 19, what is the positive value of xx?

Cevap: 5

Cevap

The positive value of xx is 5.
Solving the equation ∣3x+4∣=19|3x + 4| = 19 yields two cases: 3x+4=193x + 4 = 19, giving x=5x = 5, and 3x+4=−193x + 4 = -19, giving x=−233x = -\frac{23}{3}. The positive value among these solutions is 5.

Adım Adım Çözüm

1
Split the absolute value equation into two linear equations.
3x+4=193x + 4 = 19 or 3x+4=−193x + 4 = -19
The equation ∣a∣=b|a| = b for b≥0b \ge 0 implies a=ba = b or a=−ba = -b.
2
Solve for xx in both cases.
x=5x = 5 or x=−233x = -\frac{23}{3}
Subtract 4 from both sides and divide by 3.
3
Select the value satisfying the problem constraint.
5
The problem asks specifically for the positive value of xx.

Anahtar Kavram

Solving Linear Absolute Value Equations
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Konular

Inequalities and Absolute Value Equations

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