What is |3x-1|>= 1|2x+2| ?

The solution to |3x-1|>= 1|2x+2| is x = 3

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|3x-1|>= 1|2x+2|

∣ 3 x - 1 ∣ \geq 1 ∣ 2 x + 2 ∣

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

Interval Notation

(- \infty, - \frac{1}{5}] \cup [3, \infty)

Decimal Notation

x \leq - 0.2 or x \geq 3

Solution steps

∣ 3 x - 1 ∣ \geq 1 \cdot ∣ 2 x + 2 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

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

x^{3} + 11 x^{2} + 23 x - 35

x^{2} + 6 = 5 x

x^{2} - 64 = 63

4 + x + 2 - 2 x = 5

x^{2} - 4 x + 8 = 0

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