What is |((x^2+1))/2 |>= 3 ?

The solution to |((x^2+1))/2 |>= 3 is x = sqrt(5)

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|((x^2+1))/2 |>= 3

\frac{( x ^{2} + 1 )}{2} \geq 3

x \leq - 5 or x \geq 5

Interval Notation

(- \infty, - 5] \cup [5, \infty)

Decimal Notation

x \leq - 2.23606 \dots or x \geq 2.23606 \dots

Solution steps

\frac{x ^{2} + 1}{2} \geq 3

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

\frac{x ^{2} + 1}{2} \leq - 3 or \frac{x ^{2} + 1}{2} \geq 3

\frac{x ^{2} + 1}{2} \leq - 3 or \frac{x ^{2} + 1}{2} \geq 3

No Solution or (x \leq - 5 or x \geq 5)

Merge Overlapping Intervals

x \leq - 5 or x \geq 5

∣ 2 - 0.2 x ∣ = 2

∣ 5 w - 15 ∣ > 5

\frac{2 z}{5} = 4

6 x = 4 x^{2} - 1

- 6 x = 54

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