What is |x-2|<= 2x^2-9x+9 ?

The solution to |x-2| = (sqrt(3)+5)/2

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|x-2|<= 2x^2-9x+9

∣ x - 2 ∣ \leq 2 x^{2} - 9 x + 9

x \leq - \frac{1}{2} + 2 or x \geq \frac{3 + 5}{2}

Interval Notation

(- \infty, - \frac{1}{2} + 2] \cup [\frac{3 + 5}{2}, \infty)

Decimal Notation

x \leq 1.29289 \dots or x \geq 3.36602 \dots

Solution steps

∣ x - 2 ∣ \leq 2 x^{2} - 9 x + 9

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

x \leq - \frac{1}{2} + 2 or x \geq \frac{3 + 5}{2}

\frac{( x ^{2} - ∣ x ∣ - 12 )}{( x - 3 )} \geq 2 x

∣ t ∣ < 1

\frac{x}{( x ^{2} - x - 1 )} \leq 2

∣ 3 x - 4 ∣ > 2 - 5 x

\frac{2}{( x - 4 )} > 1

What is |x-2|<= 2x^2-9x+9 ?
The solution to |x-2|<= 2x^2-9x+9 is x<=-sqrt(1/2)+2\lor x>= (sqrt(3)+5)/2