What is |X^2-1|<= 4 ?

The solution to |X^2-1|<= 4 is -sqrt(5)<= X<= sqrt(5)

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|X^2-1|<= 4

X^{2} - 1 \leq 4

- 5 \leq X \leq 5

Interval Notation

[- 5, 5]

Decimal Notation

- 2.23606 \dots \leq X \leq 2.23606 \dots

Solution steps

X^{2} - 1 \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq X^{2} - 1 \leq 4

X^{2} - 1 \geq - 4 and X^{2} - 1 \leq 4

True for all X and - 5 \leq X \leq 5

Merge Overlapping Intervals

- 5 \leq X \leq 5

4 - \frac{4}{3}

- 2 x + 5 \leq 10

13 - \frac{3}{4} x > 13

3 x^{2} = 12 - 5 x

(\frac{2}{7})^{- 3}