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The sum of a number and negative six is greater than nine. Define a variable, write an inequality, and solve the following problem:

What is the inequality that represents the problem statement?

A. \( x - 6 < 9 \)
B. \( x + 6 > 9 \)
C. \( x - 6 > 9 \)
D. \( x + 6 < 9 \)

Answer :

Final answer:

The inequality that represents the statement 'The sum of a number and negative six is greater than nine' is x - 6 > 9. To solve for x, we add 6 to both sides, resulting in x > 15, meaning any number greater than 15 would satisfy the inequality.

Explanation:

The inequality that represents the problem statement 'The sum of a number and negative six is greater than nine' can be translated into an algebraic expression. Let's define the variable x to represent the unknown number.

The expression for the sum of x and negative six is x - 6. Since this sum is greater than nine, the inequality is written as x - 6 > 9. To solve the inequality, we will add six to both sides of the inequality:

x - 6 + 6 > 9 + 6

x > 15

This means that any number greater than 15 satisfies the inequality. Therefore, the correct inequality that represents the problem statement is Option C: x - 6 > 9.

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