Heart of Algebra: Linear Equations — Quiz 4

Questions in this quiz (10)

1. If $$\frac{1}{3}x-\frac{1}{9}x=2$$, what is the value of $$x$$?

   • 3
   • 6
   • 9
   • 12

2. What value of $$t$$ is the solution to the equation $$0.5t-0.25=4(t-0.5)+1.25$$?

   • 1/7

3. If $$\frac{x+4}{2}=\frac{x+4}{6}$$, the value of $$x+4$$ is between which of the following pairs of values?

   • $$−6$$ and $$−2$$
   • $$−2$$ and $$2$$
   • $$2$$ and $$6$$
   • $$6$$ and $$10$$

4. $$\frac{12x+28}{4}-\frac{s}{13}=r(x-8)$$In the given equation, $$s$$ and $$r$$ are constants, and $$s$$>$$0.$$ If the equation has infinitely many solutions, what is the value of $$s$$?

   • 403

5. A plant was $$5$$ inches tall when it was planted. The equation $$3n+5=20$$ can be used to find how many weeks $$n$$ it took the plant to reach a height of $$20$$ inches. Which of the following is the best interpretation of the number $$3$$ in this context?

   • The number of weeks it takes the plant to triple its height
   • The number of inches the plant grows each week
   • The height of the plant after 3 weeks
   • The total height increase of the plant

6. A candle is made of $$20$$ ounces of wax. When the candle is burning, the amount of wax decreases by $$2$$ ounces every $$5$$ hours. If $$10$$ ounces of wax remain, for how many hours has the candle been burning?

   • $$10$$
   • $$20$$
   • $$25$$
   • $$50$$

7. If $$x$$ is the solution to the equation $$2(3x-5)-7=3(x-4)+5$$, what is the value of $$x-4$$?

   • $$\frac{9}{2}$$
   • $$\frac{11}{2}$$
   • $$-\frac{2}{3}$$
   • $$\frac{15}{2}$$

8. A company calculates its monthly profit by subtracting fixed costs from its sales revenue. The equation $$12000=1.50x-3000$$ represents a month where $$x$$ items are sold. Which statement best describes $$1.50x$$ in this context?

   • The monthly profit from selling $$x$$ items
   • The monthly sales revenue from selling $$x$$ items
   • The fixed monthly cost
   • The cost of producing each item

9. The width of a rectangular garden is $$w$$ feet. The length is $$4$$ feet longer than the width. Which expression represents the perimeter, in feet, of the garden?

   • $$2w + 4$$
   • $$2w + 8$$
   • $$4w + 8$$
   • $$w^2 + 4w$$

10. What value of $$x$$ is the solution to the equation $$\frac{1}{4}(x+8)-\frac{1}{2}(x+8)=-6$$?

    • 16