What is |2x+1|+|4-3x|>18 ?

The solution to |2x+1|+|4-3x|>18 is x 21/5

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|2x+1|+|4-3x|>18

∣ 2 x + 1 ∣ + ∣ 4 - 3 x ∣ > 18

x < - 3 or x > \frac{21}{5}

Interval Notation

(- \infty, - 3) \cup (\frac{21}{5}, \infty)

Decimal Notation

x < - 3 or x > 4.2

Solution steps

∣ 2 x + 1 ∣ + ∣ 4 - 3 x ∣ > 18

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 3 or No Solution or x > \frac{21}{5}

Merge Overlapping Intervals

x < - 3 or x > \frac{21}{5}

2 (7 v + 6) \leq 14 v + 13

3 x^{2} - 9 x = x - 5

- 7 = - 1 + \frac{x}{3}

8 p^{3} - 32 p^{2} + 28 p - 112

p^{2} + 10 p = 0