How many solutions does this equation have? –8 − 7c = –7c Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equation: Analyze the equation –8 − 7c = –7c. We want to determine if there are any values of c that make this equation true.Simplify and Isolate Variable: Simplify the equation by attempting to isolate the variable c. We can try to subtract –7c from both sides of the equation to see if we can isolate c. –8 − 7c + 7c = –7c + 7cCalculate Simplification Result: Calculate the result of the simplification. –8 − 7c + 7c = 0 –8 = 0 This simplification shows that the equation –8 = 0 is not true for any value of c.Determine Number of Solutions: Determine the number of solutions based on the simplified equation. Since –8 does not equal 0, there are no values of c that can satisfy the equation. Therefore, the equation has no solution.

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How many solutions does this equation have? $\newline$ $-8 - 7c = -7c$ $\newline$ 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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-8 - 7c = -7c

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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 $–8 − 7c = –7c$ . We want to determine if there are any values of $c$ that make this equation true.
Simplify and Isolate Variable: Simplify the equation by attempting to isolate the variable $c$ . We can try to subtract $–7c$ from both sides of the equation to see if we can isolate $c$ . $–8 − 7c + 7c = –7c + 7c$
Calculate Simplification Result: Calculate the result of the simplification. $\newline$ $-8 - 7c + 7c = 0$ $\newline$ $-8 = 0$ $\newline$ This simplification shows that the equation $-8 = 0$ is not true for any value of $c$ .
Determine Number of Solutions: Determine the number of solutions based on the simplified equation. $\newline$ Since $-8$ does not equal $0$ , there are no values of $c$ that can satisfy the equation. Therefore, the equation has no solution.