What is |3x-6|<= |x-5| ?

The solution to |3x-6|<= |x-5| is 1/2 <= x<= 11/4

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|3x-6|<= |x-5|

∣ 3 x - 6 ∣ \leq ∣ x - 5 ∣

\frac{1}{2} \leq x \leq \frac{11}{4}

Solution steps

∣ 3 x - 6 ∣ \leq ∣ x - 5 ∣

Find positive and negative intervals

x < 2, 2 \leq x < 5, x \geq 5

Solve the inequality for each interval

\frac{1}{2} \leq x < 2 or 2 \leq x \leq \frac{11}{4} or No Solution

Merge Overlapping Intervals

\frac{1}{2} \leq x \leq \frac{11}{4}

∣ 2 x + 3 ∣ < ∣ x - 2 ∣

5 - 2 t = 3 t

8 \cdot 20

- 7 (n + 2) = - 14 - 7 n

\frac{13 !}{6 ! ( 13 - 6 ) !}