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do the equations x=4y+1 and x=4y - 1 have the same solution

How might you explain your answer to someone who has not learned algebra

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2 Answers

Explain this in terms of an addition problem that they do understand.

essentially: "4 apples and then add one, is that the same as 4 apples then taking one away?"

Then ask them to consider 8 apples, etc. Explain that a variable is just place holder for how ever many times you want to do the same process.

Have them put in what ever they want as the variable and let them construct the equation.

Finally have them graph out the equation using the numbers they obtained from the apple analogy. Have them do it with the equations they constructed to tie the real life situation to the abstract situation

Think to yourself that you have 4 of something then add one.  Or maybe you have 4 of something and subtract one.  Are these the same?  No.