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

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|2x+3|<10|x|

∣ 2 x + 3 ∣ < 10 ∣ x ∣

x < - \frac{1}{4} or x > \frac{3}{8}

Interval Notation

(- \infty, - \frac{1}{4}) \cup (\frac{3}{8}, \infty)

Decimal Notation

x < - 0.25 or x > 0.375

Solution steps

∣ 2 x + 3 ∣ < 10 ∣ x ∣

Find positive and negative intervals

x < - \frac{3}{2}, - \frac{3}{2} \leq x < 0, x \geq 0

Solve the inequality for each interval

x < - \frac{3}{2} or - \frac{3}{2} \leq x < - \frac{1}{4} or x > \frac{3}{8}

Merge Overlapping Intervals

x < - \frac{1}{4} or x > \frac{3}{8}

\frac{52 !}{( 52 - 7 ) ! 7 !}

8 x - 10

r^{2} + 2 r - 1 = 0

\frac{1}{4} \cdot \frac{1}{2}