What is |x-2|<3|x+7| ?

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|x-2|<3|x+7|

∣ x - 2 ∣ < 3 ∣ x + 7 ∣

x < - \frac{23}{2} or x > - \frac{19}{4}

Interval Notation

(- \infty, - \frac{23}{2}) \cup (- \frac{19}{4}, \infty)

Decimal Notation

x < - 11.5 or x > - 4.75

Solution steps

∣ x - 2 ∣ < 3 ∣ x + 7 ∣

Find positive and negative intervals

x < - 7, - 7 \leq x < 2, x \geq 2

Solve the inequality for each interval

x < - \frac{23}{2} or - \frac{19}{4} < x < 2 or x \geq 2

Merge Overlapping Intervals

x < - \frac{23}{2} or x > - \frac{19}{4}

x^{\frac{1}{2}} \cdot 2 x^{\frac{1}{2}}

- 5 (x + 9) \geq - 35

\frac{x}{2} - 2 \leq 6

0 = - 2 (5) - 5

2 6 - 4 8 + 310