What is |x+1|+|x-2|-|x-3|<x+3-|x-4| ?

The solution to |x+1|+|x-2|-|x-3|<x+3-|x-4| is 1<x<3\lor 3<x<5

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|x+1|+|x-2|-|x-3|<x+3-|x-4|

∣ x + 1 ∣ + ∣ x - 2 ∣ - ∣ x - 3 ∣ < x + 3 - ∣ x - 4 ∣

1 < x < 3 or 3 < x < 5

Interval Notation

(1, 3) \cup (3, 5)

Solution steps

∣ x + 1 ∣ + ∣ x - 2 ∣ - ∣ x - 3 ∣ < x + 3 - ∣ x - 4 ∣

Find positive and negative intervals

x < - 1, - 1 \leq x < 2, 2 \leq x < 3, 3 \leq x < 4, x \geq 4

Solve the inequality for each interval

No Solution or 1 < x < 2 or 2 \leq x < 3 or 3 < x < 4 or 4 \leq x < 5

Merge Overlapping Intervals

1 < x < 3 or 3 < x < 5

x^{4} - 5 x^{2} - 24

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

\frac{1}{5} + 2

\frac{5 x - 10}{3 x - 15}

5^{2} + 5^{2}

What is |x+1|+|x-2|-|x-3|<x+3-|x-4| ?
The solution to |x+1|+|x-2|-|x-3|<x+3-|x-4| is 1<x<3\lor 3<x<5