What is the answer to |x-1|-|x-2|+|x-3|=5x-1 ?

The answer to |x-1|-|x-2|+|x-3|=5x-1 is x= 1/2

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|x-1|-|x-2|+|x-3|=5x-1

∣ x - 1 ∣ - ∣ x - 2 ∣ + ∣ x - 3 ∣ = 5 x - 1

x = \frac{1}{2}

Solution steps

∣ x - 1 ∣ - ∣ x - 2 ∣ + ∣ x - 3 ∣ = 5 x - 1

Find positive and negative intervals

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

Solve the inequality for each interval

x = \frac{1}{2} or No Solution

x = \frac{1}{2}

\frac{( 3 x + 4 )}{3} = 7

∣ x - 4 ∣ + ∣ x - 7 ∣ = 11

x ∣ x ∣ + 7 x - 8 = 0

2 ∣ (x - 2) (x - 5) ∣ = (x - 3)^{2}

∣ x + 3 ∣ = - ∣ x + 1 ∣

What is the answer to |x-1|-|x-2|+|x-3|=5x-1 ?
The answer to |x-1|-|x-2|+|x-3|=5x-1 is x= 1/2
Solve for x: |x-1|-|x-2|+|x-3|=5x-1
The solution is x= 1/2