What is |x+6|+|x-1|<= 2x+5 ?

The solution to |x+6|+|x-1| = 1

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|x+6|+|x-1|<= 2x+5

∣ x + 6 ∣ + ∣ x - 1 ∣ \leq 2 x + 5

x \geq 1

Interval Notation

[1, \infty)

Solution steps

∣ x + 6 ∣ + ∣ x - 1 ∣ \leq 2 x + 5

Find positive and negative intervals

x < - 6, - 6 \leq x < 1, x \geq 1

Solve the inequality for each interval

No Solution or x \geq 1

Merge Overlapping Intervals

x \geq 1

x^{2} - ∣ 5 x - 3 ∣ - x < 2

\frac{( ∣ x + 4 ∣ + 2 x )}{x + 1} > 2

∣ x - 3 ∣ - ∣ x + 2 ∣ \leq 3

\frac{3 - ( 5 x - 2 )}{4} \leq 8

\frac{∣ x - 3 ∣}{∣ x + 1 ∣} \leq 1