What is the answer to |x^2-x-2|+|x+6|=|x^2-2x-8| ?

The answer to |x^2-x-2|+|x+6|=|x^2-2x-8| is x<=-6\lor-1<= x<= 2

Solve for x: |x^2-x-2|+|x+6|=|x^2-2x-8|

The solution is x<=-6\lor-1<= x<= 2

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The solution is x<=-6\lor-1<= x<= 2

x^{2} - x - 2 + ∣ x + 6 ∣ = x^{2} - 2 x - 8

x \leq - 6 or - 1 \leq x \leq 2

Solution steps

x^{2} - x - 2 + ∣ x + 6 ∣ = x^{2} - 2 x - 8

Find positive and negative intervals

x < - 6, - 6 \leq x \leq - 2, - 2 < x \leq - 1, - 1 < x < 2, 2 \leq x < 4, x \geq 4

Solve the inequality for each interval

x < - 6 or x = - 6 or x = - 1 or - 1 < x < 2 or x = 2 or No Solution

Merge Overlapping Intervals

x \leq - 6 or - 1 \leq x \leq 2

∣ x - 1 ∣ + ∣ x - 2 ∣ = 1

∣ 2 x + 1 ∣ = ∣ 4 x - 3 ∣

∣ 3 x - 4 ∣ = 0

∣ x - 1 ∣ + ∣ 2 x + 11 ∣ = 6

x^{2} + x + 1 = 5

What is the answer to |x^2-x-2|+|x+6|=|x^2-2x-8| ?
The answer to |x^2-x-2|+|x+6|=|x^2-2x-8| is x<=-6\lor-1<= x<= 2
Solve for x: |x^2-x-2|+|x+6|=|x^2-2x-8|
The solution is x<=-6\lor-1<= x<= 2