What is |2x+4|>= |x-5| ?

The solution to |2x+4|>= |x-5| is x = 1/3

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|2x+4|>= |x-5|

∣ 2 x + 4 ∣ \geq ∣ x - 5 ∣

x \leq - 9 or x \geq \frac{1}{3}

Solution steps

∣ 2 x + 4 ∣ \geq ∣ x - 5 ∣

Find positive and negative intervals

x < - 2, - 2 \leq x < 5, x \geq 5

Solve the inequality for each interval

x \leq - 9 or \frac{1}{3} \leq x < 5 or x \geq 5

Merge Overlapping Intervals

x \leq - 9 or x \geq \frac{1}{3}

∣ x - 1 ∣ + ∣ x - 5 ∣ \leq 10

\frac{x ^{2} - 1}{x ^{2} + x + 1} < 1

∣ 2 (x - 1) + 4 ∣ < 4

∣ x - 1 ∣ + ∣ x - 3 ∣ \leq 6

\frac{- 3}{x + \frac{1}{2}} < - 6