What is the answer to |x^2+6x+6|=|x^2+4x+9|+|2x-3| ?

The answer to |x^2+6x+6|=|x^2+4x+9|+|2x-3| is x>= 3/2

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|x^2+6x+6|=|x^2+4x+9|+|2x-3|

x^{2} + 6 x + 6 = x^{2} + 4 x + 9 + ∣ 2 x - 3 ∣

x \geq \frac{3}{2}

Solution steps

x^{2} + 6 x + 6 = x^{2} + 4 x + 9 + ∣ 2 x - 3 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or x \geq \frac{3}{2}

Merge Overlapping Intervals

x \geq \frac{3}{2}

x^{2} + 3 x + 2 + x + 1 = 0

x^{2} - 4 x + 2 = \frac{( 5 x - 4 )}{3}

∣ x ∣ - 2 ∣ x + 1 ∣ + 3 ∣ x + 2 ∣ = 0

x^{3} + x^{2} + x + 1 = x^{3} + 1 + x^{2} + x

∣ 2 x - 3 ∣ = ∣ 3 x + 5 ∣

What is the answer to |x^2+6x+6|=|x^2+4x+9|+|2x-3| ?
The answer to |x^2+6x+6|=|x^2+4x+9|+|2x-3| is x>= 3/2
Solve for x: |x^2+6x+6|=|x^2+4x+9|+|2x-3|
The solution is x>= 3/2