What is |x-3|-|2-3x|+|4x-5|+4>= 0 ?

The solution to |x-3|-|2-3x|+|4x-5|+4>= 0 is True for all x

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|x-3|-|2-3x|+|4x-5|+4>= 0

∣ x - 3 ∣ - ∣ 2 - 3 x ∣ + ∣ 4 x - 5 ∣ + 4 \geq 0

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

∣ x - 3 ∣ - ∣ 2 - 3 x ∣ + ∣ 4 x - 5 ∣ + 4 \geq 0

Find positive and negative intervals

x \leq \frac{2}{3}, \frac{2}{3} < x < \frac{5}{4}, \frac{5}{4} \leq x < 3, x \geq 3

Solve the inequality for each interval

x \leq \frac{2}{3} or \frac{2}{3} < x < \frac{5}{4} or \frac{5}{4} \leq x < 3 or x \geq 3

Merge Overlapping Intervals

True for all x

(x^{\frac{1}{2}}) (x)

2 x^{2} - 12 x - 14 = 0

x^{3} - 7 x^{2} + 10 x \leq 0

2 x^{2} + 2 x + 20 = 0

- 0.05518 (40) = ln \frac{N}{500}

What is |x-3|-|2-3x|+|4x-5|+4>= 0 ?
The solution to |x-3|-|2-3x|+|4x-5|+4>= 0 is True for all x