What is |x-3|<= |x-5|-|2x-3| ?

The solution to |x-3|<= |x-5|-|2x-3| is 1/2 <= x<= 5/2

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|x-3|<= |x-5|-|2x-3|

∣ x - 3 ∣ \leq ∣ x - 5 ∣ - ∣ 2 x - 3 ∣

\frac{1}{2} \leq x \leq \frac{5}{2}

Solution steps

∣ x - 3 ∣ \leq ∣ x - 5 ∣ - ∣ 2 x - 3 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

\frac{1}{2} \leq x < \frac{3}{2} or \frac{3}{2} \leq x \leq \frac{5}{2} or No Solution

Merge Overlapping Intervals

\frac{1}{2} \leq x \leq \frac{5}{2}

\frac{7}{25} \cdot \frac{5}{8}

(32 m^{5} n^{30})^{\frac{1}{5}}

4 x^{2} + 16 x + 16 = 0

2 (t + 1) = 10

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What is |x-3|<= |x-5|-|2x-3| ?
The solution to |x-3|<= |x-5|-|2x-3| is 1/2 <= x<= 5/2