How many solutions does this equation have? –3u = –4 − 3u Choices: (A)no solution (B)one solution (C)infinitely many solutions

Write Equation: Write down the given equation. –3u = –4 − 3uIsolate Variable: Attempt to isolate the variable u on one side of the equation. Add 3u to both sides of the equation to move all terms involving u to one side. –3u + 3u = –4 − 3u + 3uSimplify Equation: Simplify both sides of the equation. 0 = –4 + 0Further Simplify: Simplify the right side of the equation further. 0 = –4Analyze Solution: Analyze the simplified equation. 0 = –4 is a contradiction because 0 cannot equal –4. This means there is no value of u that will satisfy the equation.

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How many solutions does this equation have? $\newline$ $-3u = -4 - 3u$ $\newline$ 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?

\newline

-3u = -4 - 3u

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Write Equation: Write down the given equation. $\newline$ $-3u = -4 - 3u$
Isolate Variable: Attempt to isolate the variable $u$ on one side of the equation. $\newline$ Add $3u$ to both sides of the equation to move all terms involving $u$ to one side. $\newline$ $-3u + 3u = -4 - 3u + 3u$
Simplify Equation: Simplify both sides of the equation. $\newline$ $0 = -4 + 0$
Further Simplify: Simplify the right side of the equation further. $0 = -4$
Analyze Solution: Analyze the simplified equation. $\newline$ $0 = -4$ is a contradiction because $0$ cannot equal $-4$ . This means there is no value of $u$ that will satisfy the equation.