The solution to 4x-x^2>3 is 1<x<3

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4x-x^2>3

Solution

4 x - x^{2} > 3

1 < x < 3

Interval Notation

(1, 3)

Solution steps

4 x - x^{2} > 3

Rewrite in standard form

4 x - x^{2} - 3 > 0

Factor

4 x - x^{2} - 3 : - (x - 1) (x - 3)

- (x - 1) (x - 3) > 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

(x - 1) (x - 3) < 0

Identify the intervals

1 < x < 3

∣ b - 8 ∣ + 10 > 22

\frac{2 x - 1}{x - 4} \leq 3

\frac{( 6 - 2 )}{4}

3 x^{2} + 4 = 16

x^{\frac{3}{2}} \cdot x^{2}