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Answer :
To solve this problem, let's define the two integers. We'll call the greater integer [tex]\( x \)[/tex], and since the second integer is 5 less than the greater integer, it will be [tex]\( x - 5 \)[/tex].
According to the problem, the product of these two integers is 176. Therefore, we can write the equation:
[tex]\[ x(x - 5) = 176 \][/tex]
Now, let's break down this equation step-by-step:
1. Set Up the Equation:
- The integers are [tex]\( x \)[/tex] and [tex]\( x - 5 \)[/tex].
- The product of these integers is given by: [tex]\( x \times (x - 5) = 176 \)[/tex].
2. Equation to Solve:
- The equation formed is: [tex]\( x(x - 5) = 176 \)[/tex].
3. Analysis of the Equation:
- This equation can be expanded to: [tex]\( x^2 - 5x = 176 \)[/tex].
- The equation to solve for the greater integer [tex]\( x \)[/tex] is [tex]\( x(x - 5) = 176 \)[/tex].
Thus, the correct equation to find the value of [tex]\( x \)[/tex], the greater integer, is:
[tex]\[ x(x-5)=176 \][/tex]
According to the problem, the product of these two integers is 176. Therefore, we can write the equation:
[tex]\[ x(x - 5) = 176 \][/tex]
Now, let's break down this equation step-by-step:
1. Set Up the Equation:
- The integers are [tex]\( x \)[/tex] and [tex]\( x - 5 \)[/tex].
- The product of these integers is given by: [tex]\( x \times (x - 5) = 176 \)[/tex].
2. Equation to Solve:
- The equation formed is: [tex]\( x(x - 5) = 176 \)[/tex].
3. Analysis of the Equation:
- This equation can be expanded to: [tex]\( x^2 - 5x = 176 \)[/tex].
- The equation to solve for the greater integer [tex]\( x \)[/tex] is [tex]\( x(x - 5) = 176 \)[/tex].
Thus, 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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