What is |x-5|+2x-1>= |x+4| ?

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

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|x-5|+2x-1>= |x+4|

∣ x - 5 ∣ + 2 x - 1 \geq ∣ x + 4 ∣

x \geq - 4

Interval Notation

[- 4, \infty)

Solution steps

∣ x - 5 ∣ + 2 x - 1 \geq ∣ x + 4 ∣

Find positive and negative intervals

x < - 4, - 4 \leq x < 5, x \geq 5

Solve the inequality for each interval

No Solution or - 4 \leq x < 5 or x \geq 5

Merge Overlapping Intervals

x \geq - 4

x^{2} - 4 x + 3 \geq x^{2} - 6 x + 8

\frac{∣ x - 5 ∣}{∣ x + 2 ∣} < 4

x^{2} - 3 x + 2 > 2

x^{2} - 3 x + 2 > 0

∣ 3 x - 2 ∣ > 3 ∣ x - 1 ∣