What is |2x+5|>|7-4x| ?

The solution to |2x+5|>|7-4x| is 1/3 <x<6

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|2x+5|>|7-4x|

∣ 2 x + 5 ∣ > ∣ 7 - 4 x ∣

\frac{1}{3} < x < 6

Interval Notation

(\frac{1}{3}, 6)

Decimal Notation

0.33333 \dots < x < 6

Solution steps

∣ 2 x + 5 ∣ > ∣ 7 - 4 x ∣

Find positive and negative intervals

x < - \frac{5}{2}, - \frac{5}{2} \leq x \leq \frac{7}{4}, x > \frac{7}{4}

Solve the inequality for each interval

No Solution or \frac{1}{3} < x \leq \frac{7}{4} or \frac{7}{4} < x < 6

Merge Overlapping Intervals

\frac{1}{3} < x < 6

- 16 t^{2} + 96 t = 0

\frac{3}{4} x - 2 = \frac{1}{8} x

245

- 5 x^{2} + 80 x - 365 = 0

∣ 2 x + 7 ∣ < 8