Inequalities — Quiz 3

Questions in this quiz (6)

1. If $$y^2 - 4y + 3$$ < $$0$$, which of the following is the solution set for $$y$$?

   • $$-3$$ < $$y$$ < $$1$$
   • $$-1$$ < $$y$$ < $$3$$
   • $$1$$ < $$y$$ < $$3$$
   • $$1$$ < $$y$$ < $$2$$

2. If $$a \neq b$$, and the inequality $$\frac{ax - bx}{4a - 4b}$$ < $$0$$ holds, determine the set of $$x$$-values that satisfy this inequality.

   • $$(-\infty, b)$$
   • $$(-\infty, 4)$$
   • $$(-\infty, 0)$$
   • $$(-\infty, \infty)$$

3. Whenever $$(x - 2)(x + 6)$$ < $$0$$, which of the following expressions always has a negative value?

   • $$x - 4$$
   • $$x + 3$$
   • $$x - 6$$
   • $$x^2 - 9$$

4. For what values of $$x$$ is $$x^2 - 4x \geq 12$$?

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

5. If $$y$$ is a real number such that $$y^2$$ < $$2y$$, which of the following statements must be true?

   • $$y$$ > $$2$$
   • $$0$$ < $$y$$ < $$2$$
   • $$y$$ < $$-2$$
   • $$-2$$ < $$y$$ < $$2$$

6. Emma is selling tickets for a charity event. Adult tickets cost $$6$$ dollars each, and children's tickets cost $$3$$ dollars each. Emma has $$200$$ tickets available to sell and wants to make at least $$500$$ dollars. Which system of inequalities represents this scenario?

   • $$6a+3c \geq500$$$$a+c \leq200$$
   • $$6a+3c \leq500$$$$a+c \geq200$$
   • $$6a+3c=500$$$$a+c \leq200$$
   • $$3a+6c \geq500$$$$a+c=200$$