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

The solution to |6x-5|<= |3x-5| is 0<= x<= 10/9

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

∣ 6 x - 5 ∣ \leq ∣ 3 x - 5 ∣

0 \leq x \leq \frac{10}{9}

Interval Notation

[0, \frac{10}{9}]

Decimal Notation

0 \leq x \leq 1.11111 \dots

Solution steps

∣ 6 x - 5 ∣ \leq ∣ 3 x - 5 ∣

Find positive and negative intervals

x < \frac{5}{6}, \frac{5}{6} \leq x < \frac{5}{3}, x \geq \frac{5}{3}

Solve the inequality for each interval

0 \leq x < \frac{5}{6} or \frac{5}{6} \leq x \leq \frac{10}{9} or No Solution

Merge Overlapping Intervals

0 \leq x \leq \frac{10}{9}

\frac{3 ( x - 4 )}{4} - x = 1 - \frac{x}{8}

8 x^{2} + 2 x - 3 < 0

\frac{x}{2} \geq \frac{9}{x + 1} + 1

x - 1 1^{3}

y^{2} - 3 = 2 y