$3 p+4=3 p$
Part: $0 / 2$
Part 1 of 2
The equation is a conditional equation.
The equation is a contradiction.
The equation is an identity.
Answer (1)
Subtract 3 p from both sides of the equation: 3 p + 4 − 3 p = 3 p − 3 p .
Simplify the equation: 4 = 0 .
Since 4 = 0 is never true, the equation is a contradiction.
The equation is a contradiction: The equation is a contradiction.
Explanation
Understanding the Problem We are given the equation 3 p + 4 = 3 p . Our goal is to classify this equation as either a conditional equation, a contradiction, or an identity. A conditional equation is true for some values of the variable, a contradiction is never true, and an identity is always true for all values of the variable.
Subtracting 3p from Both Sides To classify the equation, we need to simplify it. We can start by subtracting 3 p from both sides of the equation: 3 p + 4 − 3 p = 3 p − 3 p
Simplifying the Equation Simplifying both sides, we get: 4 = 0
Classifying the Equation The equation 4 = 0 is never true, regardless of the value of p . Therefore, the equation is a contradiction.
Examples
Consider a scenario where you are trying to balance a budget. If you have an equation that represents your income and expenses, and simplifying that equation leads to a contradiction (like 4 = 0 ), it means there is no possible way to balance your budget with the given income and expenses. This understanding helps you recognize that you need to either increase your income or decrease your expenses to achieve a balanced budget. Recognizing contradictions in mathematical models can highlight impossible scenarios in real-world situations, prompting a re-evaluation of the initial assumptions or conditions.
