Heart of Algebra: Linear Inequalities — Quiz 1

Questions in this quiz (10)

1. The shaded region shown represents the solutions to an inequality. Which ordered pair $$(x,y)$$ is a solution to this inequality?

   • $$(-5,-6)$$
   • $$(-2,5)$$
   • $$(1,4)$$
   • $$(6,-2)$$

2. Which point $$(x,y)$$ is a solution to the system $$y\le 2x+5$$ and $$y\ge -x-2$$?

   • $$(-4,-1)$$
   • $$(0,-5)$$
   • $$(1,3)$$
   • $$(2,10)$$

3. The formula $$T=140p+50$$ gives the number of calories $$T$$ burned during exercise, where $$p$$ is the intensity level. It is recommended that $$0.4\le p\le 0.7$$. Which inequality represents the recommended range of calories burned?

   • $$106\le T\le 148$$
   • $$106\le T\le 198$$
   • $$50\le T\le 148$$
   • $$50\le T\le 198$$

4. Which of the following ordered pairs satisfies the system $$y$$ < $$4x+2$$ and $$x+y\ge 3$$?

   • $$(0,2)$$
   • $$(1,1)$$
   • $$(2,3)$$
   • $$(3,15)$$

5. A model estimates that a cyclist travels between $$15$$ and $$18$$ miles per hour. Which inequality represents the total distance $$d$$, in miles, the cyclist travels in $$5$$ hours?

   • $$15+5\le d\le 18+5$$
   • $$15(5)\le d\le 18(5)$$
   • $$15\le 5d\le 18$$
   • $$15\le d+5\le 18$$

6. The minimum value of $$x$$ is $$8$$ more than $$3$$ times a number $$k$$. Which inequality represents the possible values of $$x$$?

   • $$x$$ < $$3k+8$$
   • $$x\ge 3k+8$$
   • $$x\le 8-3k$$
   • $$x\ge 8-3k$$

7. For which table are all values solutions to $$y$$ > $$5x-2$$?

8. Four consecutive even integers are represented by $$x$$, $$x+2$$, $$x+4$$, $$x+6$$. The sum of the first and third integers is at least $$30$$. Which inequality represents this situation?

   • $$x+(x+4)\le30$$
   • $$x+(x+4)\ge30$$
   • $$x+(x+2)\ge30$$
   • $$x+(x+6)\ge30$$

9. The perimeter of a rectangle is at most $$180$$ inches. The length is $$40$$ inches and the width is $$w$$. Which inequality represents this situation?

   • $$2w+80\le180$$
   • $$2w+40\le180$$
   • $$w+80\le180$$
   • $$2w+80\ge180$$

10. A triangle has side lengths $$5$$ and $$11$$. Which inequality represents all possible values of the third side $$x$$?

    • $$x$$<$$16$$
    • $$x$$>$$16$$
    • $$6$$<$$x$$<$$16$$
    • $$x$$<$$6$$ or $$x$$>$$16$$