Questions: Solve the equation by using the rules for rewriting equations. 6-3 y=7+4 y The solution is y= (Type an integer or a simplified fraction.)

Solve the equation by using the rules for rewriting equations. 6-3 y=7+4 y The solution is y= (Type an integer or a simplified fraction.)
Transcript text: Question Solve the equation by using the rules for rewriting equations. \[ 6-3 y=7+4 y \] The solution is $y=$ $\square$ (Type an integer or a simplified fraction.)
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Solution

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Solution Steps

To solve the equation \(6 - 3y = 7 + 4y\), we need to isolate the variable \(y\). We can do this by first moving all terms involving \(y\) to one side of the equation and constant terms to the other side. This involves adding or subtracting terms from both sides of the equation. Once the terms are rearranged, we can solve for \(y\) by dividing or multiplying as necessary.

Step 1: Move Variable Terms to One Side

To solve the equation \(6 - 3y = 7 + 4y\), we first move all terms involving \(y\) to one side of the equation. We do this by adding \(3y\) to both sides:

\[ 6 = 7 + 4y + 3y \]

Step 2: Simplify the Equation

Next, we simplify the equation by combining like terms on the right side:

\[ 6 = 7 + 7y \]

Step 3: Isolate the Variable

To isolate \(y\), we subtract 7 from both sides of the equation:

\[ 6 - 7 = 7y \]

This simplifies to:

\[ -1 = 7y \]

Step 4: Solve for \(y\)

Finally, we solve for \(y\) by dividing both sides by 7:

\[ y = -\frac{1}{7} \]

Final Answer

\(\boxed{y = -\frac{1}{7}}\)

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