What is x^2+3x<5x^2-2x<4-x^2 ?

The solution to x^2+3x<5x^2-2x<4-x^2 is -2/3 <x<0

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x^2+3x<5x^2-2x<4-x^2

x^{2} + 3 x < 5 x^{2} - 2 x < 4 - x^{2}

- \frac{2}{3} < x < 0

Interval Notation

(- \frac{2}{3}, 0)

Decimal Notation

- 0.66666 \dots < x < 0

Solution steps

x^{2} + 3 x < 5 x^{2} - 2 x < 4 - x^{2}

a < u < b

then

a < u and u < b

x^{2} + 3 x < 5 x^{2} - 2 x and 5 x^{2} - 2 x < 4 - x^{2}

x^{2} + 3 x < 5 x^{2} - 2 x : x < 0 or x > \frac{5}{4}

5 x^{2} - 2 x < 4 - x^{2} : - \frac{2}{3} < x < 1

Combine the intervals

(x < 0 or x > \frac{5}{4}) and - \frac{2}{3} < x < 1

Merge Overlapping Intervals

- \frac{2}{3} < x < 0

- 1 < \frac{( 4 - 5 x )}{3} \leq 7

- 4 < 3 x + 2 \leq 5

9 < 2 - 4 x < 12

1 < 3 x - 5 < 2

- x < 3 x - 8 < x

What is x^2+3x<5x^2-2x<4-x^2 ?
The solution to x^2+3x<5x^2-2x<4-x^2 is -2/3 <x<0