What is |2x+1|+|2x-1|>5 ?

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

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|2x+1|+|2x-1|>5

∣ 2 x + 1 ∣ + ∣ 2 x - 1 ∣ > 5

x < - \frac{5}{4} or x > \frac{5}{4}

Interval Notation

(- \infty, - \frac{5}{4}) \cup (\frac{5}{4}, \infty)

Decimal Notation

x < - 1.25 or x > 1.25

Solution steps

∣ 2 x + 1 ∣ + ∣ 2 x - 1 ∣ > 5

Find positive and negative intervals

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

Solve the inequality for each interval

x < - \frac{5}{4} or No Solution or x > \frac{5}{4}

Merge Overlapping Intervals

x < - \frac{5}{4} or x > \frac{5}{4}

\frac{( x - 4 )}{( x ^{2} - 36 )} \leq 0

3 ∣ x - 3 ∣ + ∣ x + 4 ∣ \geq 12

x^{2} - 5 x + 4 - x^{2} - 4 < 0

∣ x + 2 ∣ < 4 ∣ 2 x - 3 ∣

x^{2} - ∣ x + 2 ∣ + x => 0