How many solutions does this equation have? r = 6 + 3r Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable r: Isolate the variable r on one side of the equation. r = 6 + 3r Subtract 3r from both sides to isolate r. r - 3r = 6 + 3r - 3rSimplify equation: Simplify both sides of the equation. r - 3r = 6 Combine like terms. -2r = 6Solve for r: Solve for r. Divide both sides by -2 to solve for r. -2r / -2 = 6 / -2 r = -3Check solution: Check the solution. Substitute r = -3 back into the original equation to verify if it is a solution. r = 6 + 3r -3 = 6 + 3(-3) -3 = 6 - 9 -3 = -3 The solution r = -3 satisfies the original equation.

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How many solutions does this equation have? $\newline$ $r = 6 + 3r$ $\newline$ 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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r = 6 + 3r

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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 $r$ : Isolate the variable $r$ on one side of the equation. $r = 6 + 3r$ Subtract $3r$ from both sides to isolate $r$ . $r - 3r = 6 + 3r - 3r$
Simplify equation: Simplify both sides of the equation. $r - 3r = 6$ Combine like terms. $-2r = 6$
Solve for r: Solve for r. $\newline$ Divide both sides by $-2$ to solve for r. $\newline$ $-2r / -2 = 6 / -2$ $\newline$ $r = -3$
Check solution: Check the solution. $\newline$ Substitute $r = -3$ back into the original equation to verify if it is a solution. $\newline$ $r = 6 + 3r$ $\newline$ $-3 = 6 + 3(-3)$ $\newline$ $-3 = 6 - 9$ $\newline$ $-3 = -3$ $\newline$ The solution $r = -3$ satisfies the original equation.