In Exercises 1–26, solve and check each linear equation. 7x + 4 = x + 16

검증된 단계별 안내

Start by writing down the given equation: \(7x + 4 = x + 16\).

To isolate the variable terms on one side, subtract \(x\) from both sides: \(7x - x + 4 = 16\).

Simplify the left side by combining like terms: \(6x + 4 = 16\).

Next, subtract 4 from both sides to isolate the term with \(x\): \(6x = 16 - 4\).

Finally, divide both sides by 6 to solve for \(x\): \(x = \frac{16 - 4}{6}\).

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주요 개념

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

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. It forms a straight line when graphed and typically has the form ax + b = c. Understanding how to manipulate and solve these equations is fundamental in algebra.

Solving Linear Equations

Solving a linear equation 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.

Checking Solutions

After finding a solution, substituting it back into the original equation verifies its correctness. This step ensures that no mistakes were made during solving and confirms the solution satisfies the equation.