What is |3x+1|-|3x+5|<13 ?

The solution to |3x+1|-|3x+5|<13 is True for all x

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|3x+1|-|3x+5|<13

∣ 3 x + 1 ∣ - ∣ 3 x + 5 ∣ < 13

True for all x

Solution steps

∣ 3 x + 1 ∣ - ∣ 3 x + 5 ∣ < 13

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

True for all x

\frac{- 5}{i}

3 x^{2} + 15 x + 21 = 0

\frac{n}{5} > \frac{7}{4}

- 3 < x \leq 6