The solution to 8x-15>x^2 is 3<x<5

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8x-15>x^2

Solution

8 x - 15 > x^{2}

3 < x < 5

Interval Notation

(3, 5)

Solution steps

8 x - 15 > x^{2}

Rewrite in standard form

8 x - 15 - x^{2} > 0

Factor

8 x - 15 - x^{2} : - (x - 3) (x - 5)

- (x - 3) (x - 5) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 3) (x - 5)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 3) (x - 5) < 0

Identify the intervals

3 < x < 5

- 2 = \frac{3 x - 23}{4}

20 - 6 x = 4 x - 15

(x - 9)^{2} = 9

4 = - 8 + 2 t

5 x - 4 < 3 x + 5