What is |6x-9|>= |6x+4| ?

The solution to |6x-9|>= |6x+4| is x<= 5/12

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|6x-9|>= |6x+4|

∣ 6 x - 9 ∣ \geq ∣ 6 x + 4 ∣

x \leq \frac{5}{12}

Interval Notation

(- \infty, \frac{5}{12}]

Decimal Notation

x \leq 0.41666 \dots

Solution steps

∣ 6 x - 9 ∣ \geq ∣ 6 x + 4 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

x < - \frac{2}{3} or - \frac{2}{3} \leq x \leq \frac{5}{12} or No Solution

Merge Overlapping Intervals

x \leq \frac{5}{12}

11 x^{2} + 144 x + 13

- x^{2} + 7 x - 14 = 0

6 (2 x + 1)^{2} (4 x - 1)^{2} + 8 (2 x + 1)^{3} (4 x - 1)

16 m^{4} - 25 n^{4}

- 3 (2 x - 5) < 5 (2 - x)