Questions: Solve the equation. 5x + 5/9 = 4/9 + 5x A. 1 B. no solution C. all real numbers D. 0

Solve the equation. 5x + 5/9 = 4/9 + 5x A. 1 B. no solution C. all real numbers D. 0
Transcript text: Solve the equation. \[ 5 x+\frac{5}{9}=\frac{4}{9}+5 x \] A. 1 B. no solution C. all real numbers D. 0
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Solution

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Solution Steps

To solve the equation \(5x + \frac{5}{9} = \frac{4}{9} + 5x\), we first observe that the terms involving \(x\) on both sides of the equation are identical. This means we can subtract \(5x\) from both sides, leaving us with \(\frac{5}{9} = \frac{4}{9}\). Since this statement is false, the equation has no solution.

Step 1: Simplify the Equation

The given equation is: \[ 5x + \frac{5}{9} = \frac{4}{9} + 5x \] Subtract \(5x\) from both sides to simplify: \[ \frac{5}{9} = \frac{4}{9} \]

Step 2: Analyze the Simplified Equation

The simplified equation \(\frac{5}{9} = \frac{4}{9}\) is a false statement, as \(\frac{5}{9}\) is not equal to \(\frac{4}{9}\).

Final Answer

\(\boxed{\text{no solution}}\)

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