Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2

검증된 단계별 안내

Start by expanding the left side of the equation using the distributive property: \(7(x - 4) = 7 \cdot x - 7 \cdot 4\) which simplifies to \(7x - 28\).

Rewrite the equation with the expanded left side: \(7x - 28 = x + 2\).

Next, get all the variable terms on one side and the constants on the other side. Subtract \(x\) from both sides to isolate the variable terms: \(7x - x - 28 = 2\) which simplifies to \(6x - 28 = 2\).

Then, add 28 to both sides to move the constant term: \(6x - 28 + 28 = 2 + 28\) which simplifies to \(6x = 30\).

Finally, solve for \(x\) by dividing both sides by 6: \(x = \frac{30}{6}\). After finding \(x\), analyze the solution to determine if the equation is an identity (true for all \(x\)), a conditional equation (true for specific \(x\)), or inconsistent (no solution).

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, and division. The goal is to find the value of the variable that makes the equation true.

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. Identifying the type depends on the solution set after solving the equation.

Distributive Property

The distributive property allows you to multiply a single term by each term inside parentheses, e.g., a(b + c) = ab + ac. This property is essential for simplifying expressions before solving equations.