How many solutions does this equation have? –3k = 8 − 3k Choices: (A)no solution (B)one solution (C)infinitely many solutions

Write Equation: Write down the given equation. –3k = 8 − 3kAdd Terms: Add 3k to both sides of the equation to move all the k terms to one side. –3k + 3k = 8 − 3k + 3kSimplify Equation: Simplify both sides of the equation. 0 = 8Analyze Result: Analyze the simplified equation. The equation 0 = 8 is never true, regardless of the value of k.Conclude Solution: Conclude how many solutions the equation has based on the analysis. Since 0 = 8 is a false statement, it means that there are no values of k that can satisfy the equation. Therefore, the equation has no solution.

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How many solutions does this equation have? $\newline$ $-3k = 8 - 3k$ $\newline$ 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

-3k = 8 - 3k

\newline

Choices:

\newline

(A) no solution

\newline

(B) one solution

\newline

Write Equation: Write down the given equation. $\newline$ $-3k = 8 - 3k$
Add Terms: Add $3k$ to both sides of the equation to move all the $k$ terms to one side. $\newline$ $-3k + 3k = 8 - 3k + 3k$
Simplify Equation: Simplify both sides of the equation. $0 = 8$
Analyze Result: Analyze the simplified equation. $\newline$ The equation $0 = 8$ is never true, regardless of the value of $k$ .
Conclude Solution: Conclude how many solutions the equation has based on the analysis. $\newline$ Since $0 = 8$ is a false statement, it means that there are no values of $k$ that can satisfy the equation. Therefore, the equation has no solution.