Polynomial and Rational Equations and Inequalities

Solve the inequality graphically.
2x³+3x²-17x-30<0

• (-2.5,-2)U(3,∞)
• (-∞,-2.5]U[-2,3]
• (-∞,-2.5)U(-2,3)
• [-2.5,-2]U[3,∞)

Find the solution of the inequality: $x^3-x\ge0$ 

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

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

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

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

Solve: $x^3-4x^2-x+4<0$  without a calculator.

•  $\left(-\infty,-1\right)$  

•  $\left(-1,1\right)$  

•  $\left(1,4\right)$  

•  $\left(-\infty,1\right)$  

•  $\left(4,\infty\right)$  

Solve.

Solve.

Find the solution to the inequality graphically.

• $x<0.5$

• $0.5<x<0.839$

• $x<0.5\ or\ x>0.839$

• $x>0.839$

Solve: $\frac{7}{x+3}<2$ .

•  $\left(-\infty,-3\right]\cup\left[\frac{1}{2},\infty\right]$  

•  $\left(-\infty,-3\right)\cup\left(\frac{1}{2},\infty\right)$  

•  $\left(-3,\frac{1}{2}\right)$  

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

Solve the inequality without using a calculator. Select each interval that is part of the solution. $\frac{x^2-10x+24}{x-2}\ge0$ 

•  $\left(-\infty,2\right)$  

•  $\left(-\infty,2\right]$  

•  $\left(2,4\right]$  

•  $\left[4,6\right]$  

•  $\left[6,\infty\right)$  

Find the oblique asymptote.

• y = 3x - 12
• y = x + 5
• y = 3x - 5
• y = 3x - 7

Find the oblique asymptote.
(x² - 2x - 8) / (x - 2)

• y = x
• y = x - 8
• y = x - 4
• y = x + 4