Graph each inequality. x ≤ 3

검증된 단계별 안내

Identify the inequality given: \(x \leq 3\). This means we are looking for all values of \(x\) that are less than or equal to 3.

Draw a number line and locate the point corresponding to \(x = 3\) on it.

Since the inequality includes \(x \leq 3\) (less than or equal to), use a solid dot or closed circle at \(x = 3\) to indicate that 3 is included in the solution.

Shade the number line to the left of \(x = 3\) because all values less than 3 satisfy the inequality.

Label the shaded region clearly to show that it represents all \(x\) such that \(x \leq 3\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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

Inequalities on the Number Line

An inequality like x ≤ 3 represents all values of x that are less than or equal to 3. On a number line, this includes the point 3 and all points to its left. Understanding how to represent these values visually is essential for graphing inequalities.

Closed and Open Circles

When graphing inequalities, a closed circle is used to indicate that the endpoint is included (≤ or ≥), while an open circle shows the endpoint is excluded (< or >). For x ≤ 3, a closed circle is placed at 3 to show that 3 is part of the solution.

Shading the Solution Region

After marking the boundary point, the solution region is shaded to represent all values satisfying the inequality. For x ≤ 3, the shading extends to the left of 3, indicating all numbers less than or equal to 3 are solutions.