What is |x+2|>= |x-3|-|x-2| ?

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

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|x+2|>= |x-3|-|x-2|

∣ x + 2 ∣ \geq ∣ x - 3 ∣ - ∣ x - 2 ∣

x \leq - 3 or x \geq - 1

Interval Notation

(- \infty, - 3] \cup [- 1, \infty)

Solution steps

∣ x + 2 ∣ \geq ∣ x - 3 ∣ - ∣ x - 2 ∣

Find positive and negative intervals

x < - 2, - 2 \leq x < 2, 2 \leq x < 3, x \geq 3

Solve the inequality for each interval

x \leq - 3 or - 1 \leq x < 2 or 2 \leq x < 3 or x \geq 3

Merge Overlapping Intervals

x \leq - 3 or x \geq - 1

\frac{1}{7} - \frac{1}{2}

\frac{9}{4} + \frac{9}{4}

\frac{9}{10} + \frac{3}{10}

lo g_{4} (2) = x

b - \frac{7}{4} = - \frac{2}{3}

What is |x+2|>= |x-3|-|x-2| ?
The solution to |x+2|>= |x-3|-|x-2| is x<=-3\lor x>=-1