Example Question - mathematical inequality
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Comparing Two Ratios
<p>問題のスクリーンショットが不鮮明ですが、問題の内容を読み取ることができます。問題文から、2つの比率 \(\frac{2}{5}\) と \(\frac{a}{b}\) が与えられ、\(\frac{a}{b}\) が \(\frac{2}{5}\) より小さいかどうかを判断する問題と推測されます。</p> <p>このタイプの問題を解く一般的なステップは次のとおりです：</p> <p>1. 与えられた二つの比を比較するために、共通の分母を見つけます。</p> <p>\[ 5b \]</p> <p>2. 両方の比に対して、この共通の分母で拡張します。</p> <p>\[ \frac{2}{5} \rightarrow \frac{2b}{5b} \]</p> <p>\[ \frac{a}{b} \rightarrow \frac{5a}{5b} \]</p> <p>3. 拡張された分子を比較します。</p> <p>\[ 2b \quad と \quad 5a \]</p> <p>4. 問題では \(\frac{a}{b}\) が \(\frac{2}{5}\) より小さいことが求められているので、不等式を次のように設定します。</p> <p>\[ \frac{5a}{5b} < \frac{2b}{5b} \]</p> <p>分母が等しいため、分子のみを比較すればよいので、単純な不等式として次のようになります。</p> <p>\[ 5a < 2b \]</p> <p>5. この不等式を満たす \(a\) と \(b\) の値（比率）を選ぶことで、問題の答えを見つけます。</p> <p>しかし、提供されている選択肢には \(a\) と \(b\) の具体的な値が含まれていません。そのため、これ以上の手がかりがなければ正確な答えは導き出せません。問題のスクリーンショットにすべての情報が含まれていることを確認して、完全な質問を提供してください。</p>
Writing Inequality for Given Statement
The image suggests that we need to write an inequality for a given statement. The statement is: "v is less than x, and x is less than 6". To translate this statement into a mathematical inequality, we can set up a comparison where "v" is less than "x", and "x" is also less than "6". The mathematical representation using inequality symbols would be: \[ v < x < 6 \] This is the inequality that represents the given statement, maintaining the condition to use "x" only once in the inequality.
Completing a Mathematical Inequality with Square Root
The image shows an incomplete mathematical inequality with a square root. We see \( \sqrt{68} \) and two blank spaces, one to the left and one to the right of this square root, waiting to be filled with appropriate numbers to complete the inequality. To find numbers that fit this inequality, we first need to estimate the value of \( \sqrt{68} \). Since \( 8^2 = 64 \) and \( 9^2 = 81 \), we know that \( \sqrt{68} \) falls between 8 and 9. More precisely, since 68 is closer to 64 than it is to 81, \( \sqrt{68} \) will be closer to 8 than to 9. Therefore, to satisfy the inequality, we can choose a number less than 8 for the blank on the left (for example, 7) and a number between 8 and 9 for the blank on the right (such as 8.5). So, one possible way to fill the blanks would be: \[ 7 < \sqrt{68} < 8.5 \] Note that these are just example numbers. Any number less than 8 could fit into the first blank, and any number between 8 and 9 (but not including 9) could fit into the second blank.
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