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Answer :
Let's solve the problem step-by-step:
The problem states that two positive integers have a product of 176, and one integer is 5 less than the other integer. We need to find an equation that can be used to determine [tex]\( x \)[/tex], the greater integer.
1. Let [tex]\( x \)[/tex] be the greater integer.
2. Since the other integer is 5 less than [tex]\( x \)[/tex], we can write the other integer as [tex]\( x - 5 \)[/tex].
3. The product of these two integers is given as 176. So, we can set up the equation:
[tex]\[
x \cdot (x - 5) = 176
\][/tex]
Let's simplify this equation further:
[tex]\[
x(x - 5) = 176
\][/tex]
[tex]\[
x^2 - 5x = 176
\][/tex]
This equation matches one of the given options:
[tex]\[
x(x - 5) = 176
\][/tex]
To ensure this is correct, let's consider solving the equation [tex]\( x(x - 5) = 176 \)[/tex].
From the given answer, we have the solutions:
[tex]\[
x = -11 \quad \text{or} \quad x = 16
\][/tex]
Since we are looking for positive integers, we discard [tex]\(-11\)[/tex]. Thus, the greater integer is [tex]\( 16 \)[/tex].
In conclusion, the equation that can be used to find the value of [tex]\( x \)[/tex], the greater integer, is:
[tex]\[
x(x - 5) = 176
\][/tex]
So, the correct answer is:
[tex]\[
x(x-5)=176
\][/tex]
The problem states that two positive integers have a product of 176, and one integer is 5 less than the other integer. We need to find an equation that can be used to determine [tex]\( x \)[/tex], the greater integer.
1. Let [tex]\( x \)[/tex] be the greater integer.
2. Since the other integer is 5 less than [tex]\( x \)[/tex], we can write the other integer as [tex]\( x - 5 \)[/tex].
3. The product of these two integers is given as 176. So, we can set up the equation:
[tex]\[
x \cdot (x - 5) = 176
\][/tex]
Let's simplify this equation further:
[tex]\[
x(x - 5) = 176
\][/tex]
[tex]\[
x^2 - 5x = 176
\][/tex]
This equation matches one of the given options:
[tex]\[
x(x - 5) = 176
\][/tex]
To ensure this is correct, let's consider solving the equation [tex]\( x(x - 5) = 176 \)[/tex].
From the given answer, we have the solutions:
[tex]\[
x = -11 \quad \text{or} \quad x = 16
\][/tex]
Since we are looking for positive integers, we discard [tex]\(-11\)[/tex]. Thus, the greater integer is [tex]\( 16 \)[/tex].
In conclusion, the equation that can be used to find the value of [tex]\( x \)[/tex], the greater integer, is:
[tex]\[
x(x - 5) = 176
\][/tex]
So, the correct answer is:
[tex]\[
x(x-5)=176
\][/tex]
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