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

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Q. How many solutions does this equation have?\newline−6f=−3−6f-6f = -3 - 6f\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze Equation: Analyze the equation −6f=−3−6f-6f = -3 - 6f. We can see that the term on the left side of the equation is identical to the term on the right side of the equation after the constant term −3-3.
  2. Subtract to Isolate Constant: Subtract −6f-6f from both sides of the equation to isolate the constant term.\newline−6f+6f=−3−6f+6f-6f + 6f = -3 - 6f + 6f\newlineThis simplifies to:\newline0=−30 = -3
  3. Analyzing Result: Analyze the result 0=−30 = -3. This statement is false for all values of ff, as 00 can never equal −3-3.
  4. Conclude Number of Solutions: Conclude the number of solutions.\newlineSince the statement 0=−30 = -3 is always false, it means that there are no values of ff that can satisfy the equation −6f=−3−6f-6f = -3 - 6f.

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