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Answer :
Let $x$ be the greater integer. The other integer is $x-5$. The product of the two integers is 176, so $x(x-5) = 176$. The equation that can be used to find the value of $x$, the greater integer, is $\boxed{x(x-5) = 176}$.
### Explanation
1. Setting up the equation
Let $x$ be the greater integer. Then the other integer is $x-5$. The product of these two integers is 176. Therefore, we have the equation $x(x-5) = 176$.
2. Expanding the equation
Expanding the equation, we get $x^2 - 5x = 176$. This can be rewritten as $x^2 - 5x - 176 = 0$.
3. Finding the correct option
We are looking for the equation that can be used to find the value of $x$. Comparing $x(x-5) = 176$ with the given options, we see that option c, $x(x-5) = 176$, matches our equation.
4. Final Answer
Therefore, the equation that can be used to find the value of $x$, the greater integer, is $x(x-5) = 176$.
### Examples
Understanding how to set up equations from word problems is crucial in many real-life situations. For example, if you are designing a rectangular garden where the length is 5 feet less than the width and the area is 176 square feet, you can use the equation $x(x-5) = 176$ to find the dimensions of the garden. This skill is also useful in business, finance, and engineering, where you often need to translate real-world scenarios into mathematical equations to solve problems.
### Explanation
1. Setting up the equation
Let $x$ be the greater integer. Then the other integer is $x-5$. The product of these two integers is 176. Therefore, we have the equation $x(x-5) = 176$.
2. Expanding the equation
Expanding the equation, we get $x^2 - 5x = 176$. This can be rewritten as $x^2 - 5x - 176 = 0$.
3. Finding the correct option
We are looking for the equation that can be used to find the value of $x$. Comparing $x(x-5) = 176$ with the given options, we see that option c, $x(x-5) = 176$, matches our equation.
4. Final Answer
Therefore, the equation that can be used to find the value of $x$, the greater integer, is $x(x-5) = 176$.
### Examples
Understanding how to set up equations from word problems is crucial in many real-life situations. For example, if you are designing a rectangular garden where the length is 5 feet less than the width and the area is 176 square feet, you can use the equation $x(x-5) = 176$ to find the dimensions of the garden. This skill is also useful in business, finance, and engineering, where you often need to translate real-world scenarios into mathematical equations to solve problems.
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