What is |x-1|>2|x-4| ?

The solution to |x-1|>2|x-4| is 3<x<7

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|x-1|>2|x-4|

∣ x - 1 ∣ > 2 ∣ x - 4 ∣

3 < x < 7

Interval Notation

(3, 7)

Solution steps

∣ x - 1 ∣ > 2 ∣ x - 4 ∣

Find positive and negative intervals

x < 1, 1 \leq x < 4, x \geq 4

Solve the inequality for each interval

No Solution or 3 < x < 4 or 4 \leq x < 7

Merge Overlapping Intervals

3 < x < 7

\frac{( 3 x - 5 )}{2} \geq 7

∣ 1 - x ∣ - ∣ 4 + x ∣ < 0

∣ x + 1 ∣ > 1

∣ x - 13 ∣ \leq - 2

\frac{25 ( ∣ x + 3 ∣ + x )}{( x + 2 )} > 1