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

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

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

∣ - x + 5 ∣ \geq ∣ 2 x - 1 ∣

- 4 \leq x \leq 2

Interval Notation

[- 4, 2]

Solution steps

∣ - x + 5 ∣ \geq ∣ 2 x - 1 ∣

Find positive and negative intervals

x < \frac{1}{2}, \frac{1}{2} \leq x \leq 5, x > 5

Solve the inequality for each interval

- 4 \leq x < \frac{1}{2} or \frac{1}{2} \leq x \leq 2 or No Solution

Merge Overlapping Intervals

- 4 \leq x \leq 2

\frac{\frac{3}{5}}{2}

30 < 3 x - 3 (\frac{x - 10}{2}) \leq 60

115 = x e^{0.5 l n (\frac{65}{23}) \cdot 2}

(\frac{1}{2}) y + \frac{1}{2} + 1 = y - (\frac{1}{2})^{2}

∣ x + 7 ∣ < 6