What is the answer to |x-5|+|x+6|=|2x+1| ?

The answer to |x-5|+|x+6|=|2x+1| is x = 5

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|x-5|+|x+6|=|2x+1|

∣ x - 5 ∣ + ∣ x + 6 ∣ = ∣ 2 x + 1 ∣

x \leq - 6 or x \geq 5

Solution steps

∣ x - 5 ∣ + ∣ x + 6 ∣ = ∣ 2 x + 1 ∣

Find positive and negative intervals

x < - 6, - 6 \leq x < - \frac{1}{2}, - \frac{1}{2} \leq x < 5, x \geq 5

Solve the inequality for each interval

x < - 6 or x = - 6 or No Solution or x \geq 5

Merge Overlapping Intervals

x \leq - 6 or x \geq 5

x^{2} + 4 x - 5 = x^{2} - 1

∣ x - 3 ∣ + ∣ x - 2 ∣ = 1

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

∣ x - 5 ∣ - ∣ 2 + x ∣ = 4

5 x^{2} - 3 = 2

What is the answer to |x-5|+|x+6|=|2x+1| ?
The answer to |x-5|+|x+6|=|2x+1| is x<=-6\lor x>= 5
Solve for x: |x-5|+|x+6|=|2x+1|
The solution is x<=-6\lor x>= 5