- Break the sentence into components: 'Seven plus five' becomes \(7+5\), 'is greater than' becomes \(>\), and 'six plus two' becomes \(6+2\).
- Combine these components to form the inequality \(7+5 > 6+2\).
- Verify the expression by calculating the sums: \(12 > 8\).
- Select the matching option from the list: \(\boxed{7+5 > 6+2}\).
Explanation
- Analyzing and Translating the Statement
The problem asks us to translate the English sentence "Seven plus five is greater than six plus two" into a mathematical inequality. To do this, we break the sentence down into its individual components. 'Seven' is the number 7, 'plus' is the addition operator '+', and 'five' is the number 5. Therefore, the phrase 'Seven plus five' represents the mathematical expression \(7 + 5\). Similarly, 'six' is 6, 'plus' is '+', and 'two' is 2, so 'six plus two' represents the expression \(6 + 2\). The phrase 'is greater than' translates to the inequality symbol '>'. Combining these parts, we get the mathematical statement \(7 + 5 > 6 + 2\).
- Verifying the Inequality
To confirm our translation is correct, we can evaluate both sides of the inequality. The left side is \(7 + 5\), which equals 12. The right side is \(6 + 2\), which equals 8. Since 12 is indeed greater than 8, the inequality \(12 > 8\) is a true statement. This confirms that our translation \(7 + 5 > 6 + 2\) accurately reflects the meaning of the given sentence.
- Selecting the Correct Option
Comparing our constructed inequality \(7 + 5 > 6 + 2\) with the provided options:
- \(7+5 > 6+2\)
- \(7+5 \geq 6+2\)
- \(7+5 < 6+2\)
- \(7+5 \leqslant 6+2\)
We can see that the first option matches our translation. Therefore, the correct representation for the sentence is \(7+5 > 6+2\).
Examples
Mathematical inequalities are fundamental in everyday decision-making, helping us compare quantities to determine the best choice. For instance, if you have \$10 and want to buy a snack that costs \$7 and a drink that costs \$5, you can compare the total cost (\(\$12\)) with the money you have (\(\$10\)) using the inequality \(\$12 > \$10\), which tells you that you do not have enough money. Understanding how to translate descriptive statements into mathematical inequalities allows for clear, logical analysis in real-world scenarios like budgeting, resource allocation, and logistics.