What is (6x(12+8))/5 >2x^2 ?

The solution to (6x(12+8))/5 >2x^2 is 0<x<12

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(6x(12+8))/5 >2x^2

\frac{6 x ( 12 + 8 )}{5} > 2 x^{2}

0 < x < 12

Interval Notation

(0, 12)

Solution steps

\frac{6 x ( 12 + 8 )}{5} > 2 x^{2}

Rewrite in standard form

- x^{2} + 12 x > 0

Factor

- x^{2} + 12 x : - x (x - 12)

- x (x - 12) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (x - 12)) (- 1) < 0 \cdot (- 1)

Simplify

x (x - 12) < 0

Identify the intervals

0 < x < 12

\frac{( ( x + 3 ) ^{2} \cdot ( x ^{2} + x + 1 ) )}{( ( 4 - x ) \cdot x )} \geq 0

\frac{( x ^{2} - 5 x + 6 )}{( x - 2 )} < 0

x^{2} + 6 x + 15 > 0

(x + 1 + 5)^{2} + 5 \geq 3 - (x + 1 + 3)^{2}

\frac{3}{x} < 1