What is the answer to |x-1|+|x-7|=6 ?

The answer to |x-1|+|x-7|=6 is 1<= x<= 7

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|x-1|+|x-7|=6

∣ x - 1 ∣ + ∣ x - 7 ∣ = 6

1 \leq x \leq 7

Solution steps

∣ x - 1 ∣ + ∣ x - 7 ∣ = 6

Find positive and negative intervals

x < 1, 1 \leq x < 7, x \geq 7

Solve the inequality for each interval

No Solution or 1 \leq x < 7 or x = 7

Merge Overlapping Intervals

1 \leq x \leq 7

∣ 2 x - 3 ∣ = x - 3

4 ∣ x + 44 - 3 x ∣ = 10

∣ 3 x - 5 ∣ = \frac{2}{3}

(x^{2} - 5 x + 6)^{2} - 5 x^{2} - 5 x + 6 + 6 = 0

∣ 2 x - 3 ∣ + ∣ 4 - x ∣ = ∣ x + 1 ∣