Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x-5 = 7

검증된 단계별 안내

Start with the given equation: \(2x - 5 = 7\).

Add 5 to both sides of the equation to isolate the term with \(x\): \(2x - 5 + 5 = 7 + 5\), which simplifies to \(2x = 12\).

Divide both sides of the equation by 2 to solve for \(x\): \(\frac{2x}{2} = \frac{12}{2}\), which simplifies to \(x = 6\).

Interpret the solution: since \(x = 6\) satisfies the original equation, this is a conditional equation with one solution.

Conclude that the equation is conditional because it is true for a specific value of \(x\) (namely \(x = 6\)), not for all values (identity) or no values (inconsistent).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Solving Linear Equations

Solving linear equations involves isolating the variable on one side of the equation using inverse operations such as addition, subtraction, multiplication, or division. For example, in 2x - 5 = 7, you add 5 to both sides and then divide by 2 to find x.

Types of Equations: Identity, Conditional, and Inconsistent

An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solution. After solving, you determine which type applies based on the solution set.

Checking Solutions

After finding a solution, substitute it back into the original equation to verify its validity. This step confirms whether the solution satisfies the equation, helping to classify the equation correctly.