Solving Equations 4 — Heart of Algebra

Questions in this quiz (10)

1. The equation $$(2k-1)x+7=3x-(k+5)$$, where $$k$$ is a constant, has no solution. What is the value of $$k$$?

   • $$-7$$
   • $$-5$$
   • $$2$$
   • $$3$$

2. The equation $$2(ax-3)+5=4x-(b+1)$$, where $$a$$ and $$b$$ are constants, has infinitely many solutions. What is the value of $$a+b$$?

   • $$0$$
   • $$1$$
   • $$2$$
   • $$4$$

3. In the equation $$\frac{p(x-3)}{2}-\frac{q}{3}=\frac{3x+q}{6}$$, $$p$$ and $$q$$ are constants. If the equation has infinitely many solutions for $$x$$, what is the value of $$p+q$$?

   • $$-2.5$$
   • $$-2$$
   • $$4$$
   • $$10$$

4. The equation $$a(x-2)+3b=6(b-4x)$$ has no solution, where $$a$$ and $$b$$ are constants. The constant $$b$$ cannot be equal to the value $$k$$. What is the value of $$k$$?

   • $$-24$$
   • $$-16$$
   • $$16$$
   • $$24$$

5. If $$\frac{3}{4}(2x-8)-\frac{1}{3}(9x+6)=5,$$ what is the value of $$x$$?

   • $$-\frac{26}{3}$$
   • $$-\frac{14}{3}$$
   • $$\frac{14}{3}$$
   • $$\frac{26}{3}$$

6. In the equation $$\frac{ax-1}{3}+\frac{1}{2}=2x+\frac{a}{6},$$ $$a$$ is a constant. If the equation has no solution, what is the value of $$a$$?

   • 6

7. Given the equation $$\frac{1}{2}(4x-8)-3=ax+b.$$ If this equation has infinitely many solutions, what is the value of $$a-b$$?

   • $$1$$
   • $$3$$
   • $$9$$
   • $$-5$$

8. A rectangular field has a perimeter of $$156$$ meters. The length of the field is $$12$$ meters less than three times its width. What is the width of the field, in meters?

   • 22.5

9. A chemist mixes Solution A, which is $$18\%$$ acid, with Solution B, which is $$72\%$$ acid. The chemist wants to create $$800$$ milliliters of a solution that is $$45\%$$ acid. If $$x$$ represents the number of milliliters of Solution A used, which equation can be used to determine $$x$$?

   • $$0.18x+0.72(800-x)=0.45(800)$$
   • $$0.18x+0.72x=0.45(800)$$
   • $$0.18(800)+0.72x=0.45(800)$$
   • $$0.18x+0.72(x-800)=0.45(800)$$

10. A company manufactures two types of smart devices, Type A and Type B. The production cost and selling price for each device are shown below.The company also pays a fixed monthly operating expense of $$2,400$$ dollars. Last month, the company sold a total of $$180$$ devices. If the company's profit for the month was $$24,600$$, how many Type A devices were sold?

    • 36