What is |x^2-1|<= 2 ?

The solution to |x^2-1|<= 2 is -sqrt(3)<= x<= sqrt(3)

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|x^2-1|<= 2

x^{2} - 1 \leq 2

- 3 \leq x \leq 3

Interval Notation

[- 3, 3]

Decimal Notation

- 1.73205 \dots \leq x \leq 1.73205 \dots

Solution steps

x^{2} - 1 \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq x^{2} - 1 \leq 2

x^{2} - 1 \geq - 2 and x^{2} - 1 \leq 2

True for all x and - 3 \leq x \leq 3

Merge Overlapping Intervals

- 3 \leq x \leq 3

9 x^{2} - 20 x + 4 = 0

r^{2} + r - 30 = 0

x^{4} + 5 x^{3} + 6 x^{2}

∣ 3 q - 2 ∣ = 7 - 3 q

b - 2 \geq - 1