What is |2(x+2)^2-2x^2|< 1/10 ?

The solution to |2(x+2)^2-2x^2|< 1/10 is -81/80 <x<-79/80

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|2(x+2)^2-2x^2|< 1/10

2 (x + 2)^{2} - 2 x^{2} < \frac{1}{10}

- \frac{81}{80} < x < - \frac{79}{80}

Interval Notation

(- \frac{81}{80}, - \frac{79}{80})

Decimal Notation

- 1.0125 < x < - 0.9875

Solution steps

2 (x + 2)^{2} - 2 x^{2} < \frac{1}{10}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{1}{10} < 2 (x + 2)^{2} - 2 x^{2} < \frac{1}{10}

2 (x + 2)^{2} - 2 x^{2} > - \frac{1}{10} and 2 (x + 2)^{2} - 2 x^{2} < \frac{1}{10}

x > - \frac{81}{80} and x < - \frac{79}{80}

Merge Overlapping Intervals

- \frac{81}{80} < x < - \frac{79}{80}

- 11 = p - 9

8^{2} + 1 0^{2} = x^{2}

2 x^{2} + 7 x - 2 = - x^{2} + 2 x

2 (3 x + 1) + 3 x - 2 + x = 2 (4 x - 5) + 2 (2 x - 3)

lo g_{8} (4096)

What is |2(x+2)^2-2x^2|< 1/10 ?
The solution to |2(x+2)^2-2x^2|< 1/10 is -81/80 <x<-79/80