How many solutions does this equation have? 6r = 9r − 9 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable by subtraction: Subtract 9r from both sides of the equation to isolate the variable on one side. 6r - 9r = 9r - 9 - 9r Simplifying the equation gives us: -3r = -9Solve for variable by division: Divide both sides of the equation by -3 to solve for r. -3r / -3 = -9 / -3 Simplifying the equation gives us: r = 3Check solution validity: Check if the solution r = 3 satisfies the original equation. Substitute r with 3 in the original equation: 6(3) = 9(3) - 9 18 = 27 - 9 18 = 18 Since both sides of the equation are equal, the solution r = 3 is correct.

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How many solutions does this equation have? $\newline$ $6r = 9r - 9$ $\newline$ 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

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Q. How many solutions does this equation have?

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6r = 9r - 9

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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 by subtraction: Subtract $9r$ from both sides of the equation to isolate the variable on one side. $\newline$ $6r - 9r = 9r - 9 - 9r$ $\newline$ Simplifying the equation gives us: $\newline$ $-3r = -9$
Solve for variable by division: Divide both sides of the equation by $-3$ to solve for $r$ . $\newline$ $-3r / -3 = -9 / -3$ $\newline$ Simplifying the equation gives us: $\newline$ $r = 3$
Check solution validity: Check if the solution $r = 3$ satisfies the original equation. $\newline$ Substitute $r$ with $3$ in the original equation: $\newline$ $6(3) = 9(3) - 9$ $\newline$ $18 = 27 - 9$ $\newline$ $18 = 18$ $\newline$ Since both sides of the equation are equal, the solution $r = 3$ is correct.