What is the answer to |x-3|+|4-x|=1 ?

The answer to |x-3|+|4-x|=1 is 3<= x<= 4

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|x-3|+|4-x|=1

∣ x - 3 ∣ + ∣ 4 - x ∣ = 1

3 \leq x \leq 4

Solution steps

∣ x - 3 ∣ + ∣ 4 - x ∣ = 1

Find positive and negative intervals

x < 3, 3 \leq x \leq 4, x > 4

Solve the inequality for each interval

No Solution or 3 \leq x \leq 4

Merge Overlapping Intervals

3 \leq x \leq 4

∣ x + 2 ∣ = 2 (3 - x)

∣ x - 1 ∣ + ∣ x - 3 ∣ = 2

(x + 1) (∣ x ∣ - 1) = \frac{- 1}{2}

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

x ∣ x ∣ = 4