What is the answer to |x^2-5x+6|+|x^2-x-2|=4|2-x| ?

The answer to |x^2-5x+6|+|x^2-x-2|=4|2-x| is -1<= x<= 3

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|x^2-5x+6|+|x^2-x-2|=4|2-x|

x^{2} - 5 x + 6 + x^{2} - x - 2 = 4 ∣ 2 - x ∣

- 1 \leq x \leq 3

Solution steps

x^{2} - 5 x + 6 + x^{2} - x - 2 = 4 ∣ 2 - x ∣

Find positive and negative intervals

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

Solve the inequality for each interval

x = - 1 or - 1 < x \leq 2 or 2 < x < 3 or x = 3

Merge Overlapping Intervals

- 1 \leq x \leq 3

5 x^{2} + 4 x ∣ x ∣ - 100 = 0

(x - 3)^{2} + ∣ x - 3 ∣ - 11 = 0

x^{2} - 3 x + 2 - x^{2} - 5 x + 4 = 2 x^{2} - 8 x + 6

∣ 3 x - 1 ∣ = 4

∣ x ∣ + x = 0

What is the answer to |x^2-5x+6|+|x^2-x-2|=4|2-x| ?
The answer to |x^2-5x+6|+|x^2-x-2|=4|2-x| is -1<= x<= 3
Solve for x: |x^2-5x+6|+|x^2-x-2|=4|2-x|
The solution is -1<= x<= 3