What is |2x-5|-3|x-5|+|4-x|>= 3x+5 ?

The solution to |2x-5|-3|x-5|+|4-x|>= 3x+5 is x<=-11/3

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|2x-5|-3|x-5|+|4-x|>= 3x+5

∣ 2 x - 5 ∣ - 3 ∣ x - 5 ∣ + ∣ 4 - x ∣ \geq 3 x + 5

x \leq - \frac{11}{3}

Solution steps

∣ 2 x - 5 ∣ - 3 ∣ x - 5 ∣ + ∣ 4 - x ∣ \geq 3 x + 5

Find positive and negative intervals

x < \frac{5}{2}, \frac{5}{2} \leq x \leq 4, 4 < x < 5, x \geq 5

Solve the inequality for each interval

x \leq - \frac{11}{3} or No Solution

Merge Overlapping Intervals

x \leq - \frac{11}{3}

\frac{2 x - 1}{x - 1} > 2

x^{2} - ∣ 5 x - 3 ∣ - x > 2

9 - 2 ∣ 4 x + 1 ∣ > 3

x + ∣ 3 - 2 x ∣ > ∣ x + 1 ∣ - 1

∣ x - 1 ∣^{x^{4} - 4 x^{3} + 3 x^{2}} < 1

What is |2x-5|-3|x-5|+|4-x|>= 3x+5 ?
The solution to |2x-5|-3|x-5|+|4-x|>= 3x+5 is x<=-11/3