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Answer :
To solve this problem, let's first set up the equations based on the information given.
1. Let [tex]\( x \)[/tex] be the greater integer.
2. The other integer, which is 5 less than [tex]\( x \)[/tex], can be represented as [tex]\( x - 5 \)[/tex].
3. The product of these two integers is 176. Therefore, we can write the equation:
[tex]\[
x \times (x - 5) = 176
\][/tex]
Our task is to find which equation can be used to find [tex]\( x \)[/tex], the greater integer. The equation we formulated is:
[tex]\[
x(x - 5) = 176
\][/tex]
From the choices given:
- [tex]\( x^2 + 5 = 176 \)[/tex] is incorrect because it doesn't represent the product of the integers.
- [tex]\( x(x + 5) = 176 \)[/tex] is incorrect because [tex]\( x + 5 \)[/tex] does not represent the second integer.
- [tex]\( x(x - 5) = 176 \)[/tex] is the correct equation as derived.
- [tex]\( x^2 - 5 = 176 \)[/tex] is incorrect because it does not represent the relationship between the integers correctly.
Therefore, the correct equation to find the value of [tex]\( x \)[/tex], the greater integer, is:
[tex]\[
x(x - 5) = 176
\][/tex]
1. Let [tex]\( x \)[/tex] be the greater integer.
2. The other integer, which is 5 less than [tex]\( x \)[/tex], can be represented as [tex]\( x - 5 \)[/tex].
3. The product of these two integers is 176. Therefore, we can write the equation:
[tex]\[
x \times (x - 5) = 176
\][/tex]
Our task is to find which equation can be used to find [tex]\( x \)[/tex], the greater integer. The equation we formulated is:
[tex]\[
x(x - 5) = 176
\][/tex]
From the choices given:
- [tex]\( x^2 + 5 = 176 \)[/tex] is incorrect because it doesn't represent the product of the integers.
- [tex]\( x(x + 5) = 176 \)[/tex] is incorrect because [tex]\( x + 5 \)[/tex] does not represent the second integer.
- [tex]\( x(x - 5) = 176 \)[/tex] is the correct equation as derived.
- [tex]\( x^2 - 5 = 176 \)[/tex] is incorrect because it does not represent the relationship between the integers correctly.
Therefore, the correct equation to find the value of [tex]\( x \)[/tex], the greater integer, is:
[tex]\[
x(x - 5) = 176
\][/tex]
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