What is |x-1|<|x-3| ?

The solution to |x-1|<|x-3| is x<2

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|x-1|<|x-3|

∣ x - 1 ∣ < ∣ x - 3 ∣

x < 2

Interval Notation

(- \infty, 2)

Solution steps

∣ x - 1 ∣ < ∣ x - 3 ∣

Find positive and negative intervals

x < 1, 1 \leq x < 3, x \geq 3

Solve the inequality for each interval

x < 1 or 1 \leq x < 2 or No Solution

Merge Overlapping Intervals

x < 2

3^{\frac{7}{4}}

9 x^{2} + 9 x - 2 = 14

1 - (\frac{45}{53})^{2}

8 2^{\frac{3}{2}}

\frac{2 ^{- 1}}{3}