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Determine if 3x - 12 = 3x + 1 has no solution, one solution, or infinitely many solutions
Mathematics
Grade 8
Question Content
Tell whether the equation 3x - 12 = 3x + 1 has no solution, one solution, or infinitely many solutions.
Correct Answer
No solution
Detailed Solution Steps
1
Step 1: Isolate the variable terms on one side. Subtract 3x from both sides: 3x - 3x - 12 = 3x - 3x + 1, which simplifies to -12 = 1.
2
Step 2: Analyze the result. The statement -12 = 1 is false and contains no variable. This means there is no value of x that can make the original equation true, so the equation has no solution.
Knowledge Points Involved
1
Identifying no solution for linear equations
A one-variable linear equation has no solution when simplifying leads to a false numerical statement (e.g., a = b where a ≠ b). This occurs when the coefficients of x on both sides are equal, but the constant terms are different (a = c, b ≠ d in ax + b = cx + d).
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