Pregunta
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Martin is solving the following linear equation.
His final two steps are:
Select the statement that correctly interprets Martin’s solution.
The solution is .
There are infinitely many solutions since is a false statement.
There is no solution since is a false statement.
The solution is .

Ask by King Erickson. in the United States
Mar 16,2025

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There is no solution since is a false statement.

Solución

To interpret Martin’s solution correctly, let’s analyze the steps he took in solving the equation:
  1. Starting Equation:
  2. Simplifying the Equation:
    • On the left side, combine like terms:
    • On the right side, distribute the 3:
    • So, the equation becomes:
  3. Final Steps:
    • Martin then rewrites it as:
    • Subtracting from both sides gives:
  4. Interpreting the Result:
    • The statement is clearly false. This indicates that there is no value of that can satisfy the original equation, meaning the equation has no solution.
Now, let’s evaluate the provided statements:
  • The solution is . (Incorrect)
  • There are infinitely many solutions since is a false statement. (Incorrect)
  • There is no solution since is a false statement. (Correct)
  • The solution is . (Incorrect)
Thus, the correct interpretation of Martin’s solution is:
There is no solution since is a false statement.

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Extra Insights

The statement that correctly interprets Martin’s solution is: There is no solution since is a false statement. When simplifying the equation, Martin ended up with a contradiction, indicating that there are no values of that would satisfy the original equation.
Now, to explore this further: linear equations can sometimes lead to unexpected results! When you reduce your equations and end up with something like , it means that the lines represented by the equations are parallel. Therefore, they never intersect, meaning no solutions exist. This can be a surprising and crucial learning point in algebra!

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