What is |x-1|>= ((x+1))/2 ?

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

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|x-1|>= ((x+1))/2

∣ x - 1 ∣ \geq \frac{( x + 1 )}{2}

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

Interval Notation

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

Decimal Notation

x \leq 0.33333 \dots or x \geq 3

Solution steps

∣ x - 1 ∣ \geq \frac{x + 1}{2}

Find positive and negative intervals

x < 1, x \geq 1

Solve the inequality for each interval

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

x^{2} + x > ∣ x + 2 ∣

∣ r ∣ < 1

\frac{2}{∣ x + 2 ∣} \leq 1

∣ x + 6 ∣ + ∣ x - 1 ∣ \leq 2 x + 5

x^{2} - ∣ 5 x - 3 ∣ - x < 2

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