What is |2x+1|+|3x-5|<18 ?

The solution to |2x+1|+|3x-5|<18 is -14/5 <x< 22/5

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|2x+1|+|3x-5|<18

∣ 2 x + 1 ∣ + ∣ 3 x - 5 ∣ < 18

- \frac{14}{5} < x < \frac{22}{5}

Interval Notation

(- \frac{14}{5}, \frac{22}{5})

Decimal Notation

- 2.8 < x < 4.4

Solution steps

∣ 2 x + 1 ∣ + ∣ 3 x - 5 ∣ < 18

Find positive and negative intervals

x < - \frac{1}{2}, - \frac{1}{2} \leq x < \frac{5}{3}, x \geq \frac{5}{3}

Solve the inequality for each interval

- \frac{14}{5} < x < - \frac{1}{2} or - \frac{1}{2} \leq x < \frac{5}{3} or \frac{5}{3} \leq x < \frac{22}{5}

Merge Overlapping Intervals

- \frac{14}{5} < x < \frac{22}{5}

\frac{136}{- 10 - 7}

- x^{2} + 6 x - 5

5 x^{2} - 5 x

\frac{18}{1 + 4 e ^{- 0.5 \cdot 4}}

3 n^{3} + 3 n^{2} - n - 1