Solving multi-step problems using non-linear inequalities in one variable

Which is the solution set of  $x^2+6x+7\ge0$ ?

•  $\left[-3-\sqrt{2},-3+\sqrt{2}\right]$  

•  $\left(-3-\sqrt{2},4-3+\sqrt{2}\right)$  

•  $\left(-\infty,-3-\sqrt{2}\right)\cup\left(-3+\sqrt{2},\infty\right)$  

•  $\left(-\infty,-3-\sqrt{2}\right]\cup\left[-3+\sqrt{2},\infty\right)$  

Which of the following is a quadratic inequality?

• $2x^2+2x-4=0$

• $2x+1>1$

• $x^2+1>0$

• $x^2+2x-1=0$

• Quadratic Equation

• NOT

Solve the quadratic inequality:

 $x^2-49\le0$  

•  $x\le-7\ ,\ \ x\ge7$  

•  $x\le0\ ,\ \ x\ge7$  

•  $-7\le x\le7$  

•  $-7\le x\le0$  

Solve the quadratic inequality:

 $x^2-49\ge0$  

•  $\left(-\infty,\ -7\right]\ U\ \left[7,\ \infty\right)$  

•  $x\le0\ ,\ \ x\ge7$  

•  $\left[-7,\ 7\right]$  

•  $-7\le x\le0$  

Solve:

 $2x^2+9x-143<0$  

•  $-11<x<6.5$  

•  $-11≤x≤6.5$  

• no solution

• all reals

Determine the solution of the given quadratic inequality.

 $\left(5x-3\right)\left(x+1\right)<0$  

•  $x<-1\ or\ x>\frac{3}{5}$  

•  $-1<x<\frac{3}{5}$  

Determine the solution of the given quadratic inequality.

 $\left(x+6\right)\left(4x-13\right)\le0$  

•  $x\le-6\ or\ x\ge\frac{13}{4}$  

•  $-6\le x\le\frac{13}{4}$  

x³ − 4x² + x + 6 < 0

• (-∞, -1) U (2, 3)
• (-1, 2) U (3, ∞)
• (-∞, 3)
• (-1, 3)