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Answer :
To solve this problem, we are looking for two positive integers whose product is 176, and one integer is 5 less than the other integer. We need to find an equation that describes this relationship.
Let's break it down step-by-step:
1. Define the Integers:
- Let [tex]\( x \)[/tex] be the greater integer.
- Since the other integer is 5 less than this, we can express the second integer as [tex]\( x - 5 \)[/tex].
2. Set Up the Equation Based on the Product:
- The product of these two integers is given as 176.
- Since the two integers are [tex]\( x \)[/tex] and [tex]\( x - 5 \)[/tex], their product can be expressed as:
[tex]\[
x \times (x - 5) = 176
\][/tex]
3. Choose the Correct Equation:
- The equation [tex]\( x(x - 5) = 176 \)[/tex] directly models the situation described, where [tex]\( x \)[/tex] is the greater integer and the product of the two integers is 176.
Therefore, the correct equation to use to find the value of [tex]\( x \)[/tex], the greater integer, is:
[tex]\[
x(x - 5) = 176
\][/tex]
Let's break it down step-by-step:
1. Define the Integers:
- Let [tex]\( x \)[/tex] be the greater integer.
- Since the other integer is 5 less than this, we can express the second integer as [tex]\( x - 5 \)[/tex].
2. Set Up the Equation Based on the Product:
- The product of these two integers is given as 176.
- Since the two integers are [tex]\( x \)[/tex] and [tex]\( x - 5 \)[/tex], their product can be expressed as:
[tex]\[
x \times (x - 5) = 176
\][/tex]
3. Choose the Correct Equation:
- The equation [tex]\( x(x - 5) = 176 \)[/tex] directly models the situation described, where [tex]\( x \)[/tex] is the greater integer and the product of the two integers is 176.
Therefore, the correct equation to use to find the value of [tex]\( x \)[/tex], the greater integer, is:
[tex]\[
x(x - 5) = 176
\][/tex]
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