What is 1/(|x-4|)>= 1/(|x+7|) ?

The solution to 1/(|x-4|)>= 1/(|x+7|) is -3/2 4

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1/(|x-4|)>= 1/(|x+7|)

\frac{1}{∣ x - 4 ∣} \geq \frac{1}{∣ x + 7 ∣}

- \frac{3}{2} \leq x < 4 or x > 4

Interval Notation

[- \frac{3}{2}, 4) \cup (4, \infty)

Decimal Notation

- 1.5 \leq x < 4 or x > 4

Solution steps

\frac{1}{∣ x - 4 ∣} \geq \frac{1}{∣ x + 7 ∣}

Find positive and negative intervals

x < - 7, - 7 \leq x < 4, x \geq 4

Solve the inequality for each interval

No Solution or - \frac{3}{2} \leq x < 4 or x > 4

Merge Overlapping Intervals

- \frac{3}{2} \leq x < 4 or x > 4

x^{2} + 12 x - 45

- n < 2 or 2 n - 3 > 5

(\frac{8 ^{4}}{1 0 ^{4}})^{- \frac{1}{4}}

2 x^{2} + 7 x + 5

\frac{23}{17} - \frac{5}{2}

What is 1/(|x-4|)>= 1/(|x+7|) ?
The solution to 1/(|x-4|)>= 1/(|x+7|) is -3/2 <= x<4\lor x>4