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

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

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

\frac{( x ^{2} + 1 )}{2} \geq 1

x \leq - 1 or x \geq 1

Interval Notation

(- \infty, - 1] \cup [1, \infty)

Solution steps

\frac{x ^{2} + 1}{2} \geq 1

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

\frac{x ^{2} + 1}{2} \leq - 1 or \frac{x ^{2} + 1}{2} \geq 1

\frac{x ^{2} + 1}{2} \leq - 1 or \frac{x ^{2} + 1}{2} \geq 1

No Solution or (x \leq - 1 or x \geq 1)

Merge Overlapping Intervals

x \leq - 1 or x \geq 1

\frac{1 + 3 i}{1 + i}

x^{3} - 6 x^{2} - 5 x

6 (a - 2 b) + 3 (4 a + b)

3 x^{2} - 6 x - 24

(1 0^{3})^{\frac{1}{4}}

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