What is (2x+1)(x-3)<9+(x+1)(x-4) ?

The solution to (2x+1)(x-3)<9+(x+1)(x-4) is -2<x<4

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(2x+1)(x-3)<9+(x+1)(x-4)

(2 x + 1) (x - 3) < 9 + (x + 1) (x - 4)

- 2 < x < 4

Interval Notation

(- 2, 4)

Solution steps

(2 x + 1) (x - 3) < 9 + (x + 1) (x - 4)

Rewrite in standard form

x^{2} - 2 x - 8 < 0

Factor

x^{2} - 2 x - 8 : (x + 2) (x - 4)

(x + 2) (x - 4) < 0

Identify the intervals

- 2 < x < 4

\frac{3}{2} q \leq \frac{9}{2} q - 18

x^{2} + 3 x + 6 > - 2 x + 2

3 (x - 6) - 8 x = - 2 + 5 (2 x + 1)

14 + 8

1 - (- \frac{12}{13})^{2}

What is (2x+1)(x-3)<9+(x+1)(x-4) ?
The solution to (2x+1)(x-3)<9+(x+1)(x-4) is -2<x<4