How many solutions does this equation have? 6 − 3n = –3n Choices: (A)no solution (B)one solution (C)infinitely many solutions

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How many solutions does this equation have?  6 − 3n = –3n   Choices: (A)no solution (B)one solution (C)infinitely many solutions

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Analyze Equation: Analyze the equation 6 − 3n = –3n. We want to determine if there are any values of n that make this equation true.Simplify Equation: Simplify the equation by moving all terms involving n to one side. However, we notice that both sides of the equation already have the term –3n. We can subtract –3n from both sides to potentially simplify the equation. 6 − 3n + 3n = –3n + 3nCalculate Result: Calculate the result after simplifying. 6 = 0 This simplification shows that the terms involving n cancel each other out, leaving us with a statement that does not involve n.Determine Truth Value: Determine the truth value of the simplified statement. The statement 6 = 0 is false, as 6 is not equal to 0. However, this does not affect the number of solutions to the original equation, as the n terms have canceled out.Conclude Solutions: Conclude the number of solutions based on the simplified equation. Since the n terms canceled out and we are left with a true statement (if we had 6 = 6) or a false statement (as in this case, 6 = 0), the original equation does not depend on the value of n. Therefore, the equation 6 − 3n = –3n has infinitely many solutions, as any value of n will satisfy the equation.

How many solutions does this equation have? $\newline$ $6 - 3n = -3n$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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How many solutions does this equation have?\newline6−3n=−3n6 - 3n = -3n6−3n=−3n\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

How many solutions does this equation have? $\newline$ $6 - 3n = -3n$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions