Inequalities — Heart of Algebra

Questions in this quiz (9)

1. Which of the following integers is not a solution to the inequality $$4x+9\ge-2x-15$$?

   • $$-5$$
   • $$-2$$
   • $$1$$
   • $$4$$

2. If $$-10\le 3x-4\le 8$$, which of the following must be true?

   • $$2\le x\le 4$$
   • $$-2\le x\le 4$$
   • $$-2\le x\le 6$$
   • $$2\le x\le 6$$

3. To follow her nutrition plan, Maria must limit her daily sodium intake to at most $$2300$$ milligrams. One serving of soup contains $$450$$ milligrams of sodium, and one sandwich contains $$620$$ milligrams of sodium. If Maria eats only soup servings $$s$$ and sandwiches $$w$$ in one day, which inequality represents the possible values of $$s$$ and $$w$$ that keep her within her sodium limit?

   • $$\frac{450}{s}+\frac{620}{w}\le2300$$
   • $$\frac{s}{450}+\frac{w}{620}\le2300$$
   • $$450s$$ + $$620w$$ < $$2300$$
   • $$450s+620w\le2300$$

4. If $$\frac{5}{6}x-7$$ > $$\frac{1}{3}x-15$$, which of the following must be true?

   • $$x$$ < $$-16$$
   • $$x$$ > $$24$$
   • $$x$$ < $$-24$$
   • $$x$$ > $$-16$$

5. Alex estimates that there are $$p$$ books on a library shelf. The librarian knows the actual number of books, $$a$$, and says that the actual number is within $$15$$ books inclusive of Alex’s estimate. Which of the following inequalities represents the relationship between Alex’s estimate and the actual number of books?

   • $$a+15\le p\le a-15$$
   • $$p-15\le a\le p+15$$
   • $$a\le p\le 15a$$
   • $$\frac{p}{15}\le a\le 15p$$

6. If $$k$$ is an integer and $$4(k-3)\ge -2(k+5)$$, what is the smallest possible value of $$k$$?

   • $$0$$
   • $$1$$
   • $$-1$$
   • $$3$$

7. To get to school, Maria must travel $$6$$ miles by bike and $$12$$ miles by subway each day. The bike travels at an average speed of $$x$$ miles per hour, and the subway travels at an average speed of $$y$$ miles per hour. If Maria’s total commute time is no more than $$1$$ hour, which inequality represents the possible average speeds of the bike and the subway?

   • $$\frac{6}{x}+\frac{12}{y}\le1$$
   • $$\frac{12}{x}+\frac{6}{y}\le1$$
   • $$\frac{x}{6}+\frac{y}{12}\le1$$
   • $$6x+12y\le1$$

8. If $$-\frac{15}{4}$$ < $$3x-1$$ < $$\frac{9}{4}$$ what is one possible value of $$x+2$$?

   • $$2$$
   • $$\frac{7}{2}$$
   • $$4$$
   • $$\frac{9}{2}$$

9. If $$x$$ < $$y$$, which of the following must be true?I. $$x+5$$ < $$y+5$$II. $$3x$$ < $$3y$$III. $$-y$$ < $$-x$$

   • $$I$$ only
   • $$I$$ and $$II$$ only
   • $$II$$ and $$III$$ only
   • $$I$$, $$II$$, and $$III$$