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

Analyze Equation: Analyze the equation –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.Subtract to Isolate Constant: Subtract –6f from both sides of the equation to isolate the constant term. –6f + 6f = –3 − 6f + 6f This simplifies to: 0 = –3Analyzing Result: Analyze the result 0 = –3. This statement is false for all values of f, as 0 can never equal –3.Conclude Number of Solutions: Conclude the number of solutions. Since the statement 0 = –3 is always false, it means that there are no values of f that can satisfy the equation –6f = –3 − 6f.

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

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

Q. How many solutions does this equation have?

\newline

-6f = -3 - 6f

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equation: Analyze the equation $-6f = -3 - 6f$ . 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 $-3$ .
Subtract to Isolate Constant: Subtract $-6f$ from both sides of the equation to isolate the constant term. $\newline$ $-6f + 6f = -3 - 6f + 6f$ $\newline$ This simplifies to: $\newline$ $0 = -3$
Analyzing Result: Analyze the result $0 = -3$ . This statement is false for all values of $f$ , as $0$ can never equal $-3$ .
Conclude Number of Solutions: Conclude the number of solutions. $\newline$ Since the statement $0 = -3$ is always false, it means that there are no values of $f$ that can satisfy the equation $-6f = -3 - 6f$ .