Questions: Solve the following linear equation. Identify the equation as an identity, contradiction, or conditional equation. 3(y+1)-6(y-3)=9 y+21-12 y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. The solution is the empty set. State whether the equation is an identity, contradiction, or conditional equation. Identity Contradiction Conditional equation

Solution Steps

To solve the given linear equation, we will first simplify both sides of the equation by distributing and combining like terms. Then, we will attempt to isolate the variable \( y \) to determine if there is a specific solution, if the equation holds for all values of \( y \), or if there is no solution. Based on the result, we will classify the equation as an identity, contradiction, or conditional equation.

First, we need to expand the given linear equation:

\[ 3(y+1) - 6(y-3) = 9y + 21 - 12y \]

Expanding each term:

• \(3(y+1) = 3y + 3\)
• \(-6(y-3) = -6y + 18\)

Substituting these into the equation, we have:

\[ 3y + 3 - 6y + 18 = 9y + 21 - 12y \]

Now, let's simplify both sides of the equation:

Left side:

\[ 3y + 3 - 6y + 18 = -3y + 21 \]

Right side:

\[ 9y + 21 - 12y = -3y + 21 \]

After simplification, the equation becomes:

\[ -3y + 21 = -3y + 21 \]

Both sides of the equation are identical, which means the equation holds true for all values of \(y\).

Since the equation is true for all values of \(y\), it is an identity.

Final Answer