What is |2x-5|>= |x+2| ?

The solution to |2x-5|>= |x+2| is x = 7

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|2x-5|>= |x+2|

∣ 2 x - 5 ∣ \geq ∣ x + 2 ∣

x \leq 1 or x \geq 7

Interval Notation

(- \infty, 1] \cup [7, \infty)

Solution steps

∣ 2 x - 5 ∣ \geq ∣ x + 2 ∣

Find positive and negative intervals

x < - 2, - 2 \leq x < \frac{5}{2}, x \geq \frac{5}{2}

Solve the inequality for each interval

x < - 2 or - 2 \leq x \leq 1 or x \geq 7

Merge Overlapping Intervals

x \leq 1 or x \geq 7

∣ x ∣ \leq ∣ x + 1 ∣

\frac{( x ^{2} - ∣ x ∣ - 5 )}{( ∣ x ∣ - 7 )} \geq 2 x

∣ 3 x - 2 ∣ < x + 3

∣ x - 3 ∣ > x^{2} - 3

∣ x ∣ + ∣ x - 2 ∣ \leq 6