What is (|x-49|)/(|x-7|)>15 ?

The solution to (|x-49|)/(|x-7|)>15 is 4<x<7\lor 7<x< 77/8

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(|x-49|)/(|x-7|)>15

\frac{∣ x - 49 ∣}{∣ x - 7 ∣} > 15

4 < x < 7 or 7 < x < \frac{77}{8}

Interval Notation

(4, 7) \cup (7, \frac{77}{8})

Decimal Notation

4 < x < 7 or 7 < x < 9.625

Solution steps

\frac{∣ x - 49 ∣}{∣ x - 7 ∣} > 15

Find positive and negative intervals

x < 7, 7 \leq x < 49, x \geq 49

Solve the inequality for each interval

4 < x < 7 or 7 < x < \frac{77}{8} or No Solution

Merge Overlapping Intervals

4 < x < 7 or 7 < x < \frac{77}{8}

k^{2} - 3 k - 40

1 \leq 4 - x \leq 3

w^{9} + g^{6}

2 \cdot \frac{π}{6}

82 \geq - 7 x + 2 (- 2 x - 3)

What is (|x-49|)/(|x-7|)>15 ?
The solution to (|x-49|)/(|x-7|)>15 is 4<x<7\lor 7<x< 77/8