What is the answer to |x+2|+|2x+1|-3|x-1|=6 ?

The answer to |x+2|+|2x+1|-3|x-1|=6 is x>= 1

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|x+2|+|2x+1|-3|x-1|=6

∣ x + 2 ∣ + ∣ 2 x + 1 ∣ - 3 ∣ x - 1 ∣ = 6

x \geq 1

Solution steps

∣ x + 2 ∣ + ∣ 2 x + 1 ∣ - 3 ∣ x - 1 ∣ = 6

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or x \geq 1

Merge Overlapping Intervals

x \geq 1

∣ x + 4 ∣ - ∣ x ∣ = 4

x^{2} - 9 = ∣ 3 - 4 x ∣ + 9

∣ x - 1 ∣ = ∣ 2 x - 1 ∣

∣ x - 2 ∣ + ∣ x - 6 ∣ = 2

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

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