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What number must be placed in the box in the equation below to produce an equation that has more than one solution:

 

\(\frac{1}{2}y + \frac{1}{4} = \frac{1}{12}\left(3+\boxed{\phantom{2}}~y\right)? \)

 Nov 22, 2021
 #1
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To get more than one solution, you want to create an identity; the same value on both sides of the equation.

 

I'm going to replace the box with the letter 'k'.

 

To make things simpler, multiply both sides by 12:

          6y + 3  =  3 + ky

 

This shows that k must be 6.

 Nov 22, 2021

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