What is |x+3|<2|x+5| ?

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|x+3|<2|x+5|

∣ x + 3 ∣ < 2 ∣ x + 5 ∣

x < - 7 or x > - \frac{13}{3}

Interval Notation

(- \infty, - 7) \cup (- \frac{13}{3}, \infty)

Decimal Notation

x < - 7 or x > - 4.33333 \dots

Solution steps

∣ x + 3 ∣ < 2 ∣ x + 5 ∣

Find positive and negative intervals

x < - 5, - 5 \leq x < - 3, x \geq - 3

Solve the inequality for each interval

x < - 7 or - \frac{13}{3} < x < - 3 or x \geq - 3

Merge Overlapping Intervals

x < - 7 or x > - \frac{13}{3}

- 5 < 2 x + 3 \leq 5

7 = - x + 4

x + 5 = 3 x - 63

\frac{a ^{3} + b ^{3}}{b ^{2} - a ^{2}}

3 ∣ x + 9 ∣ - 4 > 14