A labrador ran x feet at the dog park. A beagle ran 43​ less than the labrador.

Question

The labrador's tape diagram has been drawn for you. Choose the tape diagram that represents the distance the beagle ran.

x

Labrador

Beagle

x

Labrador

Beagle

Excellent!

Now write an equation to represent the distance the beagle ran. Let y represent the beagle's unknown distance.

x

Labrador

Beagle

y

y= 

x

 

−

 

43​x

Nice!

You can represent the distance the beagle ran as 

y=x−43​x.

 Now rewrite the equation using the distributive property.

x

Labrador

Beagle

y

y= x−43​x
y= 

 x

Answer 1

To represent the distance the beagle ran using the distributive property, you would start with the equation you've provided:

\[ y = x - 43 \]

This shows that the beagle ran \( y \) feet, which is \( x \) feet (the distance the labrador ran) minus 43 feet.

However, it seems you're looking to use the distributive property, which typically involves factoring or expanding expressions. In this case, the equation you have does not immediately lend itself to that since it is a simple linear equation.

If you wish to rewrite this equation in a way that applies the concept of the distributive property, you could factor out a common term (if we consider changing the format). However, given that \( x - 43 \) is already simplified, the simplest form of a distributive nature may not be directly applicable.

But to present it as a rewritten equation using a single common term for clarity's sake, you could theoretically express it differently to bring out a distribution:

\[ y = x + (-43) \]

Yet this doesn't change the original expression; it merely shows that -43 is being added in the context of \( x \).

Thus, if you're focused on expressing it directly as derived from previous steps without complicating, we can stay at:

\[ y = x - 43 \]

If you were specifically looking for a multiplication or distribution outcome, please clarify the requirement, and I'd be happy to assist further!