How many solutions does this equation have? 6q = 7q − 3 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Subtract 7q: Subtract 7q from both sides of the equation to isolate the variable on one side. 6q - 7q = 7q - 7q - 3 = -q = -3Divide by -1: Divide both sides by -1 to solve for q. -q / -1 = -3 / -1 q = 3Check solution: Check the solution by substituting q = 3 back into the original equation. 6(3) = 7(3) - 3 18 = 21 - 3 18 = 18 Since the left side equals the right side, the solution q = 3 is correct.

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How many solutions does this equation have? $\newline$ $6q = 7q - 3$ $\newline$ 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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6q = 7q - 3

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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

Subtract $7q$ : Subtract $7q$ from both sides of the equation to isolate the variable on one side. $\newline$ $6q - 7q = 7q - 7q - 3$ $\newline$ $= -q = -3$
Divide by $-1$ : Divide both sides by $-1$ to solve for q. $\newline$ $-q / -1 = -3 / -1$ $\newline$ $q = 3$
Check solution: Check the solution by substituting $q = 3$ back into the original equation. $6(3) = 7(3) - 3$ $18 = 21 - 3$ $18 = 18$ Since the left side equals the right side, the solution $q = 3$ is correct.