What is |7x-1|>10x-2 ?

The solution to |7x-1|>10x-2 is x< 1/3

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|7x-1|>10x-2

∣ 7 x - 1 ∣ > 10 x - 2

x < \frac{1}{3}

Interval Notation

(- \infty, \frac{1}{3})

Decimal Notation

x < 0.33333 \dots

Solution steps

∣ 7 x - 1 ∣ > 10 x - 2

Find positive and negative intervals

x < \frac{1}{7}, x \geq \frac{1}{7}

Solve the inequality for each interval

x < \frac{1}{7} or \frac{1}{7} \leq x < \frac{1}{3}

Merge Overlapping Intervals

x < \frac{1}{3}

4 x + 8 = 7.2 + 5 x

9 x^{2} (4 x^{2} - 3) - 4 (4 x^{2} - 3)

\frac{x}{3} > 3 + \frac{10}{3 x}

3 x^{2} + 2 x > 5