What is |x-4|>|2x-3| ?

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

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|x-4|>|2x-3|

∣ x - 4 ∣ > ∣ 2 x - 3 ∣

- 1 < x < \frac{7}{3}

Interval Notation

(- 1, \frac{7}{3})

Decimal Notation

- 1 < x < 2.33333 \dots

Solution steps

∣ x - 4 ∣ > ∣ 2 x - 3 ∣

Find positive and negative intervals

x < \frac{3}{2}, \frac{3}{2} \leq x < 4, x \geq 4

Solve the inequality for each interval

- 1 < x < \frac{3}{2} or \frac{3}{2} \leq x < \frac{7}{3} or No Solution

Merge Overlapping Intervals

- 1 < x < \frac{7}{3}

2^{4} x^{2} - 1 - 5 \geq 3

∣ 3 - 4353 x - 2.5 ∣ \geq 2

\frac{n}{2 - 4} > 3

∣ x - 6 ∣ < x^{2} - 5 x + 9

∣ x ∣ + ∣ x - 2 ∣ > 3