How many solutions does this equation have? –8k = –7k + 10 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable k: Isolate the variable k on one side of the equation. To do this, we can add 7k to both sides of the equation to get: –8k + 7k = –7k + 7k + 10 This simplifies to: –k = 10Solve for k: Solve for k. To isolate k, we multiply both sides of the equation by -1: –k * -1 = 10 * -1 This gives us: k = -10Check solution: Check the solution. We substitute k = -10 back into the original equation to verify if it is a solution: –8(-10) = –7(-10) + 10 80 = 70 + 10 80 = 80 Since both sides of the equation are equal, k = -10 is indeed a solution.

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How many solutions does this equation have? $\newline$ $-8k = -7k + 10$ $\newline$ 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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-8k = -7k + 10

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Choices:

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(A)no solution

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(B)one solution

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(C)infinitely many solutions

Isolate variable $k$ : Isolate the variable $k$ on one side of the equation. $\newline$ To do this, we can add $7k$ to both sides of the equation to get: $\newline$ $–8k + 7k = –7k + 7k + 10$ $\newline$ This simplifies to: $\newline$ $–k = 10$
Solve for k: Solve for k. $\newline$ To isolate k, we multiply both sides of the equation by $-1$ : $\newline$ $–k \times -1 = 10 \times -1$ $\newline$ This gives us: $\newline$ $k = -10$
Check solution: Check the solution. $\newline$ We substitute $k = -10$ back into the original equation to verify if it is a solution: $\newline$ $–8(-10) = –7(-10) + 10$ $\newline$ $80 = 70 + 10$ $\newline$ $80 = 80$ $\newline$ Since both sides of the equation are equal, $k = -10$ is indeed a solution.