What is |2x+1|-|6x+7|<0 ?

The solution to |2x+1|-|6x+7| -1

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|2x+1|-|6x+7|<0

∣ 2 x + 1 ∣ - ∣ 6 x + 7 ∣ < 0

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

Interval Notation

(- \infty, - \frac{3}{2}) \cup (- 1, \infty)

Decimal Notation

x < - 1.5 or x > - 1

Solution steps

∣ 2 x + 1 ∣ - ∣ 6 x + 7 ∣ < 0

Find positive and negative intervals

x < - \frac{7}{6}, - \frac{7}{6} \leq x < - \frac{1}{2}, x \geq - \frac{1}{2}

Solve the inequality for each interval

x < - \frac{3}{2} or - 1 < x < - \frac{1}{2} or x \geq - \frac{1}{2}

Merge Overlapping Intervals

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

14 x^{3} + 21 x^{2}

6 x^{2} - 5 x + 4 = 0

24 p + 6 + 4 qp + q

25 - (x + 2)^{2}

6 \cdot 15