What is the answer to |x-1|+|4-x|=6 ?

The answer to |x-1|+|4-x|=6 is x=-1/2 \lor x= 11/2

Solve for x: |x-1|+|4-x|=6

The solution is x=-1/2 \lor x= 11/2

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∣ x - 1 ∣ + ∣ 4 - x ∣ = 6

x = - \frac{1}{2} or x = \frac{11}{2}

Decimal Notation

x = - 0.5, x = 5.5

Solution steps

∣ x - 1 ∣ + ∣ 4 - x ∣ = 6

Find positive and negative intervals

x < 1, 1 \leq x \leq 4, x > 4

Solve the inequality for each interval

x = - \frac{1}{2} or No Solution or x = \frac{11}{2}

x = - \frac{1}{2} or x = \frac{11}{2}

x^{2} - 5 ∣ x - 1 ∣ - 1 = 0

4 - 2 ∣ x - 1 ∣ = 7

∣ 3 x - 9 ∣ = 7 x - 29

∣ 4 - 3 x ∣ = ∣ - 4 ∣

x^{2} + 7 ∣ x ∣ + 10 = 0

What is the answer to |x-1|+|4-x|=6 ?
The answer to |x-1|+|4-x|=6 is x=-1/2 \lor x= 11/2
Solve for x: |x-1|+|4-x|=6
The solution is x=-1/2 \lor x= 11/2