Classify each of the following equations.
$6(x-1)+13-x=5x+7$

• A. Conditional
• B. Identity
• C. Contradiction

Answer: (B)

Verified step by step guidance

1. Start by expanding the expression on the left side of the equation: \(6\left(x - 1\right) + 13 - x = 5x + 7\). Use the distributive property to multiply 6 by each term inside the parentheses.
2. After expanding, combine like terms on the left side to simplify the expression. This means adding or subtracting the terms that contain \(x\) and the constant terms separately.
3. Next, bring all terms involving \(x\) to one side of the equation and all constant terms to the other side. This helps isolate the variable and makes it easier to analyze the equation.
4. Simplify both sides of the equation after moving terms. If the variable terms cancel out and you are left with a true statement (like \(a = a\)), the equation is an identity. If you get a false statement (like \(a = b\) where \(a \neq b\)), it is a contradiction. Otherwise, it is conditional.
5. Based on the simplified form, classify the equation as either an identity (true for all \(x\)), a contradiction (no solution), or conditional (true for some specific \(x\) values).