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Answer :
To solve this problem, we need to find which equation can be used to determine the value of [tex]\( x \)[/tex], the greater integer.
Here’s a step-by-step explanation:
1. Understand the Problem:
- We have two positive integers whose product is 176.
- One integer is 5 less than the other integer.
2. Define the Variables:
- Let the greater integer be [tex]\( x \)[/tex].
- Then, the smaller integer, being 5 less than the greater integer, would be [tex]\( x - 5 \)[/tex].
3. Set Up the Equation:
- According to the problem, the product of the two integers is 176.
- Therefore, we can write the equation as:
[tex]\[
x \cdot (x - 5) = 176
\][/tex]
4. Choose the Correct Equation:
- The equation [tex]\( x(x-5) = 176 \)[/tex] describes the relationship correctly: the product of [tex]\( x \)[/tex] and [tex]\( x-5 \)[/tex] equals 176.
By following these steps, we can determine that the appropriate equation for finding the greater integer [tex]\( x \)[/tex] is:
[tex]\[
x(x-5) = 176
\][/tex]
Here’s a step-by-step explanation:
1. Understand the Problem:
- We have two positive integers whose product is 176.
- One integer is 5 less than the other integer.
2. Define the Variables:
- Let the greater integer be [tex]\( x \)[/tex].
- Then, the smaller integer, being 5 less than the greater integer, would be [tex]\( x - 5 \)[/tex].
3. Set Up the Equation:
- According to the problem, the product of the two integers is 176.
- Therefore, we can write the equation as:
[tex]\[
x \cdot (x - 5) = 176
\][/tex]
4. Choose the Correct Equation:
- The equation [tex]\( x(x-5) = 176 \)[/tex] describes the relationship correctly: the product of [tex]\( x \)[/tex] and [tex]\( x-5 \)[/tex] equals 176.
By following these steps, we can determine that the appropriate equation for finding the greater integer [tex]\( x \)[/tex] is:
[tex]\[
x(x-5) = 176
\][/tex]
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