x(x – 5) = 176 is the correct equation to find the greater integer.
As the question mentions, the greater integer is x. So, the smaller integer will be (x - 5). Also, we are informed that their product is 176.
Now, representing the given information as mathematical expression -
x(x – 5) = 176
On further multiplication on Left Hand Side, we get the equation -
x² - 5x = 176
Rewriting the equation -
x² - 5x - 176 = 0
Further solving the equation to validate it.
x² - 16x + 11x - 176 = 0
x (x - 16) + 11 (x - 16) = 0
(x - 16) (x + 11) = 0
x = 16, -11
As stated, the integers are positive. So, the value of x and hence greater integer is 16.
Value of small integer = 16 - 5
Value of small integer = 11
So, the two integers are 16 and 11. Their product is 176 hence, our formed equation is correct.
Therefore, the equation that can be used to find x is : x(x – 5) = 176.
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The complete question is -
Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of x, the greater integer?
x² + 5 = 176
x(x + 5) = 176
x(x – 5) = 176
x² – 5 = 176
