What is the answer to |x^2-x+1|+|2x-3|=4x ?

The answer to |x^2-x+1|+|2x-3|=4x is x=(7-sqrt(33))/2 \lor x=(3+sqrt(17))/2

Solve for x: |x^2-x+1|+|2x-3|=4x

The solution is x=(7-sqrt(33))/2 \lor x=(3+sqrt(17))/2

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x^{2} - x + 1 + ∣ 2 x - 3 ∣ = 4 x

x = \frac{7 - 33}{2} or x = \frac{3 + 17}{2}

Solution steps

x^{2} - x + 1 + ∣ 2 x - 3 ∣ = 4 x

Find positive and negative intervals

x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

x = \frac{7 - 33}{2} or x = \frac{3 + 17}{2}

(- x^{2} + x - 1) 3 + x^{2} - x + 1 = 0

(x + 3) ∣ x + 2 ∣ + ∣ 2 x + 3 ∣ + 1 = 0

∣ x - 2 ∣ + ∣ x - 4 ∣ = 5

13 + ∣ x ∣ = ∣ - 6 ∣ + 17

∣ - x ∣ = 5

What is the answer to |x^2-x+1|+|2x-3|=4x ?
The answer to |x^2-x+1|+|2x-3|=4x is x=(7-sqrt(33))/2 \lor x=(3+sqrt(17))/2
Solve for x: |x^2-x+1|+|2x-3|=4x
The solution is x=(7-sqrt(33))/2 \lor x=(3+sqrt(17))/2