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In Mathematics / High School | 2025-07-04

Identify the equation as a conditional equation, contradiction, or an identity. Then solve:

[tex]3 p+4=3 p[/tex]

Asked by yea83

Answer (2)

The equation 3 p + 4 = 3 p simplifies to 4 = 0 , which is a false statement. Therefore, it is classified as a contradiction. The final conclusion is that the equation has no solutions.
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Answered by Anonymous | 2025-07-04

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 a false statement, the equation is a contradiction.
The equation is a contradiction ​ .

Explanation

Understanding the Types of Equations We are given the equation 3 p + 4 = 3 p and we need to classify it as either a conditional equation, a contradiction, or an identity. Let's analyze each type:


Conditional Equation: An equation that is true for only some values of the variable.
Contradiction: An equation that is never true for any value of the variable.
Identity: An equation that is always true for all values of the variable.


Subtracting 3p from Both Sides To determine the type of equation, we will try to simplify it by performing algebraic manipulations. We 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

Identifying the Equation Type The equation 4 = 0 is a false statement, regardless of the value of p . This means that there is no value of p that can make the original equation 3 p + 4 = 3 p true. Therefore, the equation is a contradiction.

Final Answer The equation 3 p + 4 = 3 p simplifies to 4 = 0 , which is always false. Thus, the equation is a contradiction.


Examples
Consider a scenario where you are trying to balance a budget. If the equation represents a financial constraint, a contradiction would mean that the budget is impossible to balance, no matter how you adjust the variables. For example, if 'p' represents spending and the equation implies that spending an amount '3p' plus an additional fixed cost of 4 always equals spending just '3p', it's an impossible scenario. This highlights the importance of identifying contradictions in mathematical models to avoid pursuing unachievable solutions.

Answered by GinnyAnswer | 2025-07-04

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