What is |10x-1|-1<7x ?

The solution to |10x-1|-1<7x is 0<x< 2/3

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|10x-1|-1<7x

∣ 10 x - 1 ∣ - 1 < 7 x

0 < x < \frac{2}{3}

Interval Notation

(0, \frac{2}{3})

Decimal Notation

0 < x < 0.66666 \dots

Solution steps

∣ 10 x - 1 ∣ - 1 < 7 x

Find positive and negative intervals

x < \frac{1}{10}, x \geq \frac{1}{10}

Solve the inequality for each interval

0 < x < \frac{1}{10} or \frac{1}{10} \leq x < \frac{2}{3}

Merge Overlapping Intervals

0 < x < \frac{2}{3}

\frac{1}{3} (x^{2} - 9) = 24

2 y^{2} + 13 y + 6

x^{2} + 8 x + 64 = 12

56 \cdot 83

4 x^{2} + (5 - 2 x)^{2} = 17