How many solutions does this equation have? 9c = –7 + 8c Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable c: Isolate the variable c on one side of the equation. To do this, subtract 8c from both sides of the equation. 9c - 8c = –7 + 8c - 8cSimplify both sides: Simplify both sides of the equation. 9c - 8c = 1c –7 + 8c - 8c = –7 So, the equation simplifies to: 1c = –7Determine number of solutions: Determine the number of solutions. Since we have a non-zero coefficient (1) for c and a constant on the other side (–7), this equation has one unique solution for c.

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How many solutions does this equation have? $\newline$ $9c = -7 + 8c$ $\newline$ 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

9c = -7 + 8c

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Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Isolate variable c: Isolate the variable $c$ on one side of the equation. $\newline$ To do this, subtract $8c$ from both sides of the equation. $\newline$ $9c - 8c = -7 + 8c - 8c$
Simplify both sides: Simplify both sides of the equation. $\newline$ $9c - 8c = 1c$ $\newline$ $–7 + 8c - 8c = –7$ $\newline$ So, the equation simplifies to: $\newline$ $1c = –7$
Determine number of solutions: Determine the number of solutions. $\newline$ Since we have a non-zero coefficient ( $1$ ) for $c$ and a constant on the other side ( $-7$ ), this equation has one unique solution for $c$ .