How many solutions does this equation have? –10k − 1 = –10k Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equation: Analyze the equation –10k − 1 = –10k. We want to determine if there are any values of k that make this equation true.Isolate Variable: Attempt to isolate the variable k on one side of the equation. Subtract –10k from both sides of the equation to see if we can simplify it. (–10k − 1) - (–10k) = (–10k) - (–10k)Simplify Equation: Simplify both sides of the equation. On the left side, –10k cancels out with +10k, leaving us with just –1. On the right side, –10k cancels out with +10k, leaving us with 0. So we have –1 = 0.Check Validity: Determine if the simplified equation makes sense. The equation –1 = 0 is never true, as –1 and 0 are not equal. This means there are no values of k that can satisfy the equation.

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How many solutions does this equation have? $\newline$ $-10k - 1 = -10k$ $\newline$ 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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-10k - 1 = -10k

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Choices:

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(A) no solution

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(B) one solution

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Analyze Equation: Analyze the equation $–10k − 1 = –10k$ . We want to determine if there are any values of $k$ that make this equation true.
Isolate Variable: Attempt to isolate the variable $k$ on one side of the equation. $\newline$ Subtract $–10k$ from both sides of the equation to see if we can simplify it. $\newline$ $(–10k − 1) - (–10k) = (–10k) - (–10k)$
Simplify Equation: Simplify both sides of the equation. $\newline$ On the left side, $-10k$ cancels out with $+10k$ , leaving us with just $-1$ . $\newline$ On the right side, $-10k$ cancels out with $+10k$ , leaving us with $0$ . $\newline$ So we have $-1 = 0$ .
Check Validity: Determine if the simplified equation makes sense. $\newline$ The equation $–1 = 0$ is never true, as $–1$ and $0$ are not equal. $\newline$ This means there are no values of $k$ that can satisfy the equation.