How many solutions does this equation have? –3r + 7 = –2r Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable r: Isolate the variable r on one side of the equation. To do this, we can add 3r to both sides of the equation to get rid of the –3r on the left side. –3r + 7 + 3r = –2r + 3r This simplifies to: 7 = rCheck solution validity: Check if the simplified equation makes sense. We have isolated r and found that r = 7. This is a valid solution and there is no contradiction in the equation.Determine number of solutions: Determine the number of solutions. Since we have found a specific value for r (r = 7), there is only one solution to the equation.

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How many solutions does this equation have? $\newline$ $-3r + 7 = -2r$ $\newline$ 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?

\newline

-3r + 7 = -2r

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Isolate variable r: Isolate the variable r on one side of the equation. $\newline$ To do this, we can add $3r$ to both sides of the equation to get rid of the $-3r$ on the left side. $\newline$ $-3r + 7 + 3r = -2r + 3r$ $\newline$ This simplifies to: $\newline$ $7 = r$
Check solution validity: Check if the simplified equation makes sense. $\newline$ We have isolated $r$ and found that $r = 7$ . This is a valid solution and there is no contradiction in the equation.
Determine number of solutions: Determine the number of solutions. $\newline$ Since we have found a specific value for $r$ ( $r = 7$ ), there is only $1$ solution to the equation.