Solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)

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Distribute the terms inside the brackets and parentheses. Start with the innermost parentheses: expand \(4(x - 3)\) to \(4x - 12\). Then simplify \([4x - 12 - 5]\) to \(4x - 17\). Finally, simplify \{2x - (4x - 17)\} to \{2x - 4x + 17\}, which becomes \(-2x + 17\).

Substitute the simplified expression \(-2x + 17\) back into the original equation. The equation becomes \(4x + 13 - (-2x + 17) = 2(x - 6)\).

Simplify the left-hand side of the equation by combining like terms: \(4x + 13 + 2x - 17\) simplifies to \(6x - 4\). The equation now reads \(6x - 4 = 2(x - 6)\).

Distribute the \(2\) on the right-hand side: \(2(x - 6)\) becomes \(2x - 12\). The equation now reads \(6x - 4 = 2x - 12\).

Isolate \(x\) by first subtracting \(2x\) from both sides: \(6x - 2x - 4 = -12\), which simplifies to \(4x - 4 = -12\). Then add \(4\) to both sides: \(4x = -8\). Finally, divide both sides by \(4\) to solve for \(x\).

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주요 개념

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

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property is essential for simplifying expressions where a term is multiplied by a sum or difference. In the given equation, applying the distributive property will help in expanding terms like 2(x - 6) and 4(x - 3) effectively.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This step is crucial in simplifying equations to make them easier to solve. In the equation provided, after applying the distributive property, you will need to combine terms involving 'x' and constant terms to isolate the variable.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This typically includes isolating the variable on one side of the equation through operations such as addition, subtraction, multiplication, or division. Understanding the steps to isolate 'x' in the given equation is key to finding the solution.