What is the answer to |x-3|+|x+2|-|x-4|=3 ?

The answer to |x-3|+|x+2|-|x-4|=3 is x=-6\lor x=2

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|x-3|+|x+2|-|x-4|=3

∣ x - 3 ∣ + ∣ x + 2 ∣ - ∣ x - 4 ∣ = 3

x = - 6 or x = 2

Solution steps

∣ x - 3 ∣ + ∣ x + 2 ∣ - ∣ x - 4 ∣ = 3

Find positive and negative intervals

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

Solve the inequality for each interval

x = - 6 or x = 2 or No Solution

x = - 6 or x = 2

∣ x - 1 ∣ + ∣ x - 2 ∣ = 2

∣ x ∣ + 2 ∣ x - 6 ∣ = 12

∣ z ∣ + ∣ z - 4 ∣ = 6

∣ x + 2 ∣ = ∣ 2 x - 3 ∣

2 x - x^{2} - 3 = 1

What is the answer to |x-3|+|x+2|-|x-4|=3 ?
The answer to |x-3|+|x+2|-|x-4|=3 is x=-6\lor x=2
Solve for x: |x-3|+|x+2|-|x-4|=3
The solution is x=-6\lor x=2