In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 4(3x - 2) - 3x < 3(1 + 3x) - 7

검증된 단계별 안내

Start by expanding both sides of the inequality: expand \(4(3x - 2)\) and \(3(1 + 3x)\) to remove the parentheses.

After expansion, combine like terms on each side to simplify the inequality.

Next, get all terms containing \(x\) on one side of the inequality and constant terms on the other side by adding or subtracting terms accordingly.

Isolate the variable \(x\) by dividing or multiplying both sides of the inequality by the coefficient of \(x\). Remember, if you multiply or divide by a negative number, you must reverse the inequality sign.

Express the solution set in interval notation and then graph the solution on a number line, showing all values of \(x\) that satisfy the inequality.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

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

Solving Linear Inequalities

Linear inequalities involve expressions with variables raised to the first power and inequality symbols like <, >, ≤, or ≥. Solving them requires isolating the variable on one side by performing algebraic operations, similar to solving linear equations, but with attention to inequality rules.

Properties of Inequalities

When solving inequalities, adding or subtracting the same number on both sides preserves the inequality direction. However, multiplying or dividing both sides by a negative number reverses the inequality sign. Understanding these properties is essential to maintain correct solution sets.

Interval Notation and Graphing Solutions

Interval notation expresses solution sets as intervals on the number line, using parentheses for strict inequalities and brackets for inclusive inequalities. Graphing these solutions visually represents the range of values satisfying the inequality, aiding in interpretation and communication.