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Answer :
To solve this problem, let's break it down step-by-step:
1. Understand the problem:
We have two positive integers with a product of 176, and one integer is 5 less than the other. Our task is to find an equation that helps determine the greater integer, [tex]\( x \)[/tex].
2. Define variables:
- Let [tex]\( x \)[/tex] be the greater integer.
- Therefore, the other integer, being 5 less, is [tex]\( x - 5 \)[/tex].
3. Form an equation from the given conditions:
- We know the product of these two integers is 176. So, we can write the equation:
[tex]\[
x \times (x - 5) = 176
\][/tex]
4. Simplify and verify the equation:
- The equation [tex]\( x(x - 5) = 176 \)[/tex] directly represents the relationship stated in the problem where [tex]\( x \)[/tex] is multiplied by [tex]\( (x - 5) \)[/tex], giving the product 176.
Thus, the correct equation to use is:
[tex]\[
x(x - 5) = 176
\][/tex]
This equation is formed based on the given relationships and conditions in the problem statement.
1. Understand the problem:
We have two positive integers with a product of 176, and one integer is 5 less than the other. Our task is to find an equation that helps determine the greater integer, [tex]\( x \)[/tex].
2. Define variables:
- Let [tex]\( x \)[/tex] be the greater integer.
- Therefore, the other integer, being 5 less, is [tex]\( x - 5 \)[/tex].
3. Form an equation from the given conditions:
- We know the product of these two integers is 176. So, we can write the equation:
[tex]\[
x \times (x - 5) = 176
\][/tex]
4. Simplify and verify the equation:
- The equation [tex]\( x(x - 5) = 176 \)[/tex] directly represents the relationship stated in the problem where [tex]\( x \)[/tex] is multiplied by [tex]\( (x - 5) \)[/tex], giving the product 176.
Thus, the correct equation to use is:
[tex]\[
x(x - 5) = 176
\][/tex]
This equation is formed based on the given relationships and conditions in the problem statement.
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