Question

solve the equation for ( r ). justify each step.

equation: ( c = 2pi r )
explanation: write the equation.
reason: given

empty boxes for equation and explanation steps

options (for steps and reasons):

• ( r = 2pi c )
• ( \frac{c}{r} = 2pi )
• ( \frac{c}{2pi} = r )
• ( r = \frac{c}{2pi} )
• rewrite the equation.
• multiply each side by ( 2pi ).
• divide each side by ( r ).
• divide each side by ( 2pi ).
• division property of equality
• symmetric property of equality

Explanation:

Step1: State the given equation

$C = 2\pi r$

Step2: Divide by $2\pi$ (isolate $r$)

$\frac{C}{2\pi} = \frac{2\pi r}{2\pi}$

Step3: Simplify to solve for $r$

$\frac{C}{2\pi} = r$

Step4: Apply symmetric property

$r = \frac{C}{2\pi}$

Answer:

Equation	Explanation	Reason
$\frac{C}{2\pi} = r$	Divide each side by $2\pi$.	Division Property of Equality
$r = \frac{C}{2\pi}$	Rewrite the equation.	Symmetric Property of Equality