How many solutions does this equation have? –2v − 3 = –2v Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equation: Analyze the equation –2v − 3 = –2v. We want to find out if there are any values of v that make this equation true.Isolate Variable: Attempt to isolate the variable v on one side of the equation. Subtract –2v from both sides of the equation to see if we can simplify it. –2v − 3 + 2v = –2v + 2vSimplify Equation: Simplify both sides of the equation. On the left side, –2v and +2v cancel each other out, leaving us with just –3. On the right side, –2v and +2v also cancel each other out, leaving us with 0. So we have –3 = 0.Check Validity: Determine if the simplified equation makes sense. The equation –3 = 0 is never true because –3 is not equal to 0. This means there are no values of v that can satisfy the equation.

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How many solutions does this equation have? $\newline$ $-2v - 3 = -2v$ $\newline$ 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?

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-2v - 3 = -2v

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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 $–2v − 3 = –2v$ . We want to find out if there are any values of $v$ that make this equation true.
Isolate Variable: Attempt to isolate the variable $v$ on one side of the equation. $\newline$ Subtract $–2v$ from both sides of the equation to see if we can simplify it. $\newline$ $–2v − 3 + 2v = –2v + 2v$
Simplify Equation: Simplify both sides of the equation. $\newline$ On the left side, $–2v$ and $+2v$ cancel each other out, leaving us with just $–3$ . $\newline$ On the right side, $–2v$ and $+2v$ also cancel each other out, leaving us with $0$ . $\newline$ So we have $–3 = 0$ .
Check Validity: Determine if the simplified equation makes sense. $\newline$ The equation $–3 = 0$ is never true because $–3$ is not equal to $0$ . $\newline$ This means there are no values of $v$ that can satisfy the equation.