What is 2|2x-3|<|x+10| ?

The solution to 2|2x-3|<|x+10| is -4/5 <x< 16/3

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2|2x-3|<|x+10|

2 ∣ 2 x - 3 ∣ < ∣ x + 10 ∣

- \frac{4}{5} < x < \frac{16}{3}

Interval Notation

(- \frac{4}{5}, \frac{16}{3})

Decimal Notation

- 0.8 < x < 5.33333 \dots

Solution steps

2 ∣ 2 x - 3 ∣ < ∣ x + 10 ∣

Find positive and negative intervals

x < - 10, - 10 \leq x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

No Solution or - \frac{4}{5} < x < \frac{3}{2} or \frac{3}{2} \leq x < \frac{16}{3}

Merge Overlapping Intervals

- \frac{4}{5} < x < \frac{16}{3}

23 - 5 x \leq 3

\frac{m ^{4} - n ^{4}}{m ^{2} + n ^{2}}

2 m^{2} - m - 15 = 0

(12 x + 7)^{2} - 4 (2 x - 1)^{2}