What is |5x|<|10-5x| ?

The solution to |5x|<|10-5x| is x<1

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|5x|<|10-5x|

∣ 5 x ∣ < ∣ 10 - 5 x ∣

x < 1

Solution steps

∣ 5 x ∣ < ∣ 10 - 5 x ∣

Find positive and negative intervals

x < 0, 0 \leq x \leq 2, x > 2

Solve the inequality for each interval

x < 0 or 0 \leq x < 1 or No Solution

Merge Overlapping Intervals

x < 1

x^{2} - 3 x + ∣ x + 1 ∣ \geq 4

\frac{( x - 4 )}{( x + 2 )} \leq \frac{( x - 2 )}{( x - 1 )}

x^{2} + x - 6 < 6

∣ x - 1 ∣ \geq ∣ x - 3 ∣

(1 + x)^{2} \geq 1 - x^{2}