How many solutions does this equation have? –8f + 2 = –9f Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable f: Isolate the variable f on one side of the equation. To do this, we can add 9f to both sides of the equation to get: –8f + 9f + 2 = –9f + 9f This simplifies to: f + 2 = 0Solve for f: Solve for f. Subtract 2 from both sides of the equation to isolate f: f + 2 - 2 = 0 - 2 This simplifies to: f = -2Check solution: Check the solution. Substitute f = -2 back into the original equation to verify if it holds true: –8(-2) + 2 = –9(-2) 16 + 2 = 18 18 = 18 Since the left-hand side equals the right-hand side, the solution f = -2 is correct.

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How many solutions does this equation have? $\newline$ $-8f + 2 = -9f$ $\newline$ 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

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Q. How many solutions does this equation have?

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-8f + 2 = -9f

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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

Isolate variable $f$ : Isolate the variable $f$ on one side of the equation. $\newline$ To do this, we can add $9f$ to both sides of the equation to get: $\newline$ $–8f + 9f + 2 = –9f + 9f$ $\newline$ This simplifies to: $\newline$ $f + 2 = 0$
Solve for f: Solve for f. $\newline$ Subtract $2$ from both sides of the equation to isolate $f$ : $\newline$ $f + 2 - 2 = 0 - 2$ $\newline$ This simplifies to: $\newline$ $f = -2$
Check solution: Check the solution. $\newline$ Substitute $f = -2$ back into the original equation to verify if it holds true: $\newline$ $–8(-2) + 2 = –9(-2)$ $\newline$ $16 + 2 = 18$ $\newline$ $18 = 18$ $\newline$ Since the left-hand side equals the right-hand side, the solution $f = -2$ is correct.