How many solutions does this equation have? –9f = –9f − 1 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze the equation: Analyze the equation –9f = –9f − 1. We have the same term on both sides of the equation, –9f, but on the right side, there is an additional –1. This suggests that the equation is claiming that –9f is equal to itself minus 1, which is a contradiction.Simplify and rearrange: Try to simplify or rearrange the equation to see if it can be true. If we add 9f to both sides of the equation to try to isolate the variable, we get: –9f + 9f = –9f + 9f − 1 0 = 0 − 1 This simplifies to: 0 = –1Determine if solution makes sense: Determine if the simplified equation makes sense. The equation 0 = –1 is never true for any value of f. This means that there is no value of f that can satisfy the original equation –9f = –9f − 1.

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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?

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-9f = -9f - 1

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Choices:

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(A)no solution

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(B)one solution

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(C)infinitely many solutions

Analyze the equation: Analyze the equation $–9f = –9f − 1$ . We have the same term on both sides of the equation, $–9f$ , but on the right side, there is an additional $–1$ . This suggests that the equation is claiming that $–9f$ is equal to itself minus $1$ , which is a contradiction.
Simplify and rearrange: Try to simplify or rearrange the equation to see if it can be true. $\newline$ If we add $9f$ to both sides of the equation to try to isolate the variable, we get: $\newline$ $-9f + 9f = -9f + 9f - 1$ $\newline$ $0 = 0 - 1$ $\newline$ This simplifies to: $\newline$ $0 = -1$
Determine if solution makes sense: Determine if the simplified equation makes sense. $\newline$ The equation $0 = -1$ is never true for any value of $f$ . This means that there is no value of $f$ that can satisfy the original equation $-9f = -9f - 1$ .