How many solutions does this equation have? –7u − 1 = –7u Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equation: Analyze the equation –7u − 1 = –7u. We want to determine if there are any values of u that make this equation true.Isolate Variable: Attempt to isolate the variable u on one side of the equation. Subtract –7u from both sides of the equation to see if we can simplify it. (–7u − 1) - (–7u) = (–7u) - (–7u)Simplify Equation: Simplify both sides of the equation. On the left side, –7u cancels out with –7u, leaving us with just –1. On the right side, –7u cancels out with –7u, 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 because –1 is not equal to 0. This means there are no values of u that can satisfy the equation.

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How many solutions does this equation have? $\newline$ $-7u - 1 = -7u$ $\newline$ 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

-7u - 1 = -7u

\newline

Choices:

\newline

(A) no solution

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(B) one solution

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Analyze Equation: Analyze the equation $–7u − 1 = –7u$ . We want to determine if there are any values of $u$ that make this equation true.
Isolate Variable: Attempt to isolate the variable $u$ on one side of the equation. $\newline$ Subtract $-7u$ from both sides of the equation to see if we can simplify it. $\newline$ $(-7u - 1) - (-7u) = (-7u) - (-7u)$
Simplify Equation: Simplify both sides of the equation. $\newline$ On the left side, $-7u$ cancels out with $-7u$ , leaving us with just $-1$ . $\newline$ On the right side, $-7u$ cancels out with $-7u$ , 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 because $–1$ is not equal to $0$ . $\newline$ This means there are no values of $u$ that can satisfy the equation.