What is 5/(6(x+2)-4)< x/(3+12) ?

The solution to 5/(6(x+2)-4) (sqrt(466)-4)/6

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5/(6(x+2)-4)< x/(3+12)

\frac{5}{6 ( x + 2 ) - 4} < \frac{x}{3 + 12}

- \frac{4 + 466}{6} < x < - \frac{4}{3} or x > \frac{466 - 4}{6}

Interval Notation

(- \frac{4 + 466}{6}, - \frac{4}{3}) \cup (\frac{466 - 4}{6}, \infty)

Decimal Notation

- 4.26450 \dots < x < - 1.33333 \dots or x > 2.93117 \dots

Solution steps

\frac{5}{6 ( x + 2 ) - 4} < \frac{x}{3 + 12}

Rewrite in standard form

\frac{75 - 2 x ( 3 x + 4 )}{3 x + 4} < 0

Factor

\frac{75 - 2 x ( 3 x + 4 )}{3 x + 4} : \frac{- ( x - \frac{- 4 + 466}{6} ) ( x + \frac{4 + 466}{6} )}{3 x + 4}

\frac{- ( x - \frac{- 4 + 466}{6} ) ( x + \frac{4 + 466}{6} )}{3 x + 4} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - \frac{- 4 + 466}{6} ) ( x + \frac{4 + 466}{6} ) ) ( - 1 )}{3 x + 4} > 0 \cdot (- 1)

Simplify

\frac{( x - \frac{- 4 + 466}{6} ) ( x + \frac{4 + 466}{6} )}{3 x + 4} > 0

Identify the intervals

- \frac{4 + 466}{6} < x < - \frac{4}{3} or x > \frac{466 - 4}{6}

3 \cdot (x - 1)^{2} - 12 \leq 6 x^{2} - (3 + x)^{2}

\frac{( ( x + 1 ) ^{2} + 1 )}{x} > 0

\frac{( x ^{2} - 5 x + 4 )}{( x ^{2} - 1 )} \leq 1

x (x + 2) - x^{2} > 4 x - 7

\frac{( 6 + j ^{3} )}{( 2 - j ^{3} ) + 8} < \frac{3}{10}

What is 5/(6(x+2)-4)< x/(3+12) ?
The solution to 5/(6(x+2)-4)< x/(3+12) is -(4+sqrt(466))/6 <x<-4/3 \lor x>(sqrt(466)-4)/6