What is |3x-5|+|x+1|>= 5 ?

The solution to |3x-5|+|x+1|>= 5 is x = 9/4

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|3x-5|+|x+1|>= 5

∣ 3 x - 5 ∣ + ∣ x + 1 ∣ \geq 5

x \leq \frac{1}{2} or x \geq \frac{9}{4}

Interval Notation

(- \infty, \frac{1}{2}] \cup [\frac{9}{4}, \infty)

Decimal Notation

x \leq 0.5 or x \geq 2.25

Solution steps

∣ 3 x - 5 ∣ + ∣ x + 1 ∣ \geq 5

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 1 or - 1 \leq x \leq \frac{1}{2} or x \geq \frac{9}{4}

Merge Overlapping Intervals

x \leq \frac{1}{2} or x \geq \frac{9}{4}

1 < \frac{3 x - 2}{x + 1} < 4

2 m^{4} - 10 m^{2} - 28

∣ 2 y - 7 ∣ \geq 14

(x + 2)^{2} (x + 5) (x + 9) \geq 0

y^{2} - 4 y + 20 = 0

What is |3x-5|+|x+1|>= 5 ?
The solution to |3x-5|+|x+1|>= 5 is x<= 1/2 \lor x>= 9/4