Solving Equations 1 — Heart of Algebra

Questions in this quiz (10)

1. If $$3(a+b+2c+4d-2)=5a+3b+6c+12d$$, find the value of $$a$$.

   • $$-6$$
   • $$-3$$
   • $$3b+6c+12d$$
   • $$6c+12d$$

2. If $$x$$ > $$0$$ and $$y$$ > $$0$$, the equation $$\sqrt{xy}=x-y$$ is equivalent to which of the following?

   • $$xy=x^2-y^2$$
   • $$xy=x^2+y^2$$
   • $$2xy=x^2-y^2$$
   • $$3xy=x^2+y^2$$

3. If $$\frac{7}{4}x=\frac{21}{8}$$, what is the value of $$x$$?

   • $$\frac{4}{7}$$
   • $$\frac{21}{4}$$
   • $$\frac{3}{2}$$
   • $$\frac{4}{21}$$

4. The variable $$y$$ is defined by the equation $$y=\frac{x}{2x-d}$$. Which of the following expresses $$x$$ in terms of $$y$$ and $$d$$?

   • $$\frac{dy}{1-2y}$$
   • $$\frac{dy}{2y-1}$$
   • $$\frac{d(1-y)}{2y}$$
   • $$\frac{2y+1}{dy}$$

5. If $$4x+6y=12$$, what is the value of $$2x+3y$$?

   • $$3$$
   • $$5$$
   • $$6$$
   • $$12$$

6. If $$\frac{a}{b}=4$$, what is the value of $$\frac{2b}{3a}$$?

   • $$\frac{1}{6}$$
   • $$\frac{1}{4}$$
   • $$\frac{3}{8}$$
   • $$\frac{2}{3}$$

7. If $$\frac{2+3x}{1-y}=\frac{1}{4}$$, find $$y$$ in terms of $$x$$.

   • $$y=-4x+8$$
   • $$y=-12x-7$$
   • $$y=7x+8$$
   • $$y=8x+7$$

8. If $$a^m=b$$, find $$a^{3m}$$ in terms of $$b$$.

   • $$3b$$
   • $$\frac{b}{3}$$
   • $$b^{3m}$$
   • $$b^3$$

9. If $$4x-5=7$$, what is the value of $$(x-1)^3$$?

   • $$-8$$
   • $$-1$$
   • $$8$$
   • $$27$$

10. If $$y$$ < $$0$$ and $$y^2-20=5$$, what is the value of $$y$$?

    • $$-5$$
    • $$-3$$
    • $$3$$
    • $$5$$