Nonlinear & Rational Inequalites

Solve the inequality in interval notation

 $x^2-9\le0$  

•  $\left(-\infty,-3\right)\cup\left(3,\infty\right)$  

•  $\left(-3,3\right)$  

•  $\left[-\infty,-3\right]\cup\left[3,\infty\right]$  

•  $\left[-3,3\right]$  

Solve the inequality in interval notation

 $\frac{x+2}{x-4}\ge3$  

•  $\left(-\infty,4\right)\cup\left(7,\infty\right)$  

•  $\left(4,7\right]$  

•  $\left[-\infty,4\right]\cup\left[7,\infty\right]$  

•  $\left[4,7\right)$  

Solve the inequality in interval notation

 $x^2-x-12>0$  

•  $\left(-\infty,-3\right)\cup\left(4,\infty\right)$  

•  $\left(-3,4\right)$  

•  $\left[-\infty,-3\right]\cup\left[4,\infty\right]$  

•  $\left[-3,4\right]$  

Solve the inequality in interval notation

 $\frac{3x^2}{x^2+4}\ge1.5$  

•  $\left(-\infty,-2\right)\cup\left(2,\infty\right)$  

•  $\left(-2,2\right)$  

•  $\left(-\infty,-2\right]\cup\left[2,\infty\right)$  

•  $\left[-2,2\right]$  

Solve the inequality in interval notation

 $-x^2-11x+12<0$  

•  $\left(-\infty,-12\right)\cup\left(1,\infty\right)$  

•  $\left(-12,1\right)$  

•  $\left(-\infty,-12\right]\cup\left[1,\infty\right)$  

•  $\left[-12,1\right]$  

Solve the inequality in interval notation

 $\frac{x+6}{x+1}-2\ge0$  

•  $\left(-\infty,-1\right)\cup\left(4,\infty\right)$  

•  $\left(-1,4\right]$  

•  $\left(-\infty,-1\right]\cup\left[4,\infty\right)$  

•  $\left[-1,4\right]$  

Solve the inequality in interval notation

 $x^2-8x+15>0$  

•  $\left(-\infty,3\right)\cup\left(5,\infty\right)$  

•  $\left(3,5\right)$  

•  $\left(-\infty,3\right]\cup\left[5,\infty\right)$  

•  $\left[3,5\right]$  

Solve the inequality in interval notation

 $\frac{5+7x}{1+2x}\ge4$  

•  $\left(-\infty,-\frac{1}{2}\right)\cup\left(1,\infty\right)$  

•  $\left(-\frac{1}{2},1\right]$  

•  $\left(-\infty,-\frac{1}{2}\right]\cup\left[1,\infty\right)$  

•  $\left[-\frac{1}{2},1\right)$  

Solve the inequality in interval notation

 $2x^3+2x^2-4x\le0$  

•  $\left[-\infty,-2\right]\cup\left[0,1\right]$  

•  $\left(-\infty,-2\right)\cup\left(0,1\right)$  

•  $\left(-\infty,-2\right]\cup\left[0,1\right]$  

•  $\left(-\infty,-2\right)\cup\left[0,1\right]$  

Solve the inequality in interval notation

 $x^3-2x^2-11x+12\ge0$  

•  $\left[-3,1\right]\cup\left[4,\infty\right]$  

•  $\left(-3,1\right)\cup\left(4,\infty\right)$  

•  $\left(-3,1\right]\cup\left[4,\infty\right)$  

•  $\left[-3,1\right]\cup\left[4,\infty\right)$