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Answer :
To solve the problem, we need to find an equation that represents the relationship between the two positive integers given that their product is 176 and one integer is 5 less than the other.
1. Identify the integers:
- Let's call the greater integer [tex]\( x \)[/tex].
- Since one integer is 5 less than the other, the smaller integer will be [tex]\( x - 5 \)[/tex].
2. Set up the equation for the product:
- According to the problem, the product of these two integers is 176. So, we can write the equation for the product as:
[tex]\[
x(x - 5) = 176
\][/tex]
3. Choose the correct equation:
- Considering the options provided:
- [tex]\( x^2 + 5 = 176 \)[/tex]
- [tex]\( x(x + 5) = 176 \)[/tex]
- [tex]\( x(x - 5) = 176 \)[/tex]
- [tex]\( x^2 - 5 = 176 \)[/tex]
- The equation [tex]\( x(x - 5) = 176 \)[/tex] accurately represents the situation where the greater integer is [tex]\( x \)[/tex] and the smaller integer is [tex]\( x - 5\)[/tex], making the correct choice.
Thus, the equation that can be used to find the value of [tex]\( x \)[/tex], the greater integer, is [tex]\( x(x - 5) = 176 \)[/tex].
1. Identify the integers:
- Let's call the greater integer [tex]\( x \)[/tex].
- Since one integer is 5 less than the other, the smaller integer will be [tex]\( x - 5 \)[/tex].
2. Set up the equation for the product:
- According to the problem, the product of these two integers is 176. So, we can write the equation for the product as:
[tex]\[
x(x - 5) = 176
\][/tex]
3. Choose the correct equation:
- Considering the options provided:
- [tex]\( x^2 + 5 = 176 \)[/tex]
- [tex]\( x(x + 5) = 176 \)[/tex]
- [tex]\( x(x - 5) = 176 \)[/tex]
- [tex]\( x^2 - 5 = 176 \)[/tex]
- The equation [tex]\( x(x - 5) = 176 \)[/tex] accurately represents the situation where the greater integer is [tex]\( x \)[/tex] and the smaller integer is [tex]\( x - 5\)[/tex], making the correct choice.
Thus, the equation that can be used to find the value of [tex]\( x \)[/tex], the greater integer, is [tex]\( x(x - 5) = 176 \)[/tex].
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