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

Which graph matches the inequality  $-x^2-3x+4\le0$  

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Find the interval over which the following is true:

 $0.25x^2+x+1<4$  

•  $\left(-6,2\right)$  

•  $\left[-6,2\right]$  

•  $\left(-\infty,-6\right)\cup\left(2,\infty\right)$  

•  $\left(-\infty,-6\right]\cup\left[2,\infty\right)$  
  

Solve the quadratic inequality x^2 - 5x + 6 > 0.

• x^2 - 5x + 6 < 0

• x^2 - 5x + 6 = 0

• x^2 - 5x + 6 = 1

Solve:

3x - x² > 0

• (−∞, 0) U (3, ∞)

• (−∞, - 3) U (0, ∞)

• (-3, 0)

• (0, 3)

Which of the following is the solution of the given Quadratic Inequality?

x² + 9x + 13 > -7

hint: move the -7 to make the quadratic inequality "equal" to zero

• x < -5 or x > -4

• x > -5 or x < -4

• x < 5 or x > 4

• x > 5 or x < 4

x² - 2x - 15 ≤ 0

• x ≤ -3 or x ≥ 5

• -3 ≤ x ≤ 5

• x = -3, 5

• x ≥ -3

Determine the solution of the given quadratic inequality.

 $\left(5x-9\right)\left(x-2\right)>0$  

•  $x<\frac{9}{5}\ or\ x>2$  

•  $\frac{9}{5}<x<2$