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Answer :
To solve this problem, we need to find the correct equation that represents the relationship given in the problem between two integers.
Let's break down the information:
1. We have two integers. Let's call one integer [tex]\( x \)[/tex].
2. According to the problem, the other integer is "four more than three times" the first integer. In mathematical terms, this can be expressed as [tex]\( 3x + 4 \)[/tex].
3. The product of these two integers is 112.
Now, let's formulate the equation:
- The product of the integers can be expressed as:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
- Expanding the left side, we have:
[tex]\[
x \times (3x + 4) = 3x^2 + 4x
\][/tex]
- Therefore, the equation becomes:
[tex]\[
3x^2 + 4x = 112
\][/tex]
This matches option A, which is [tex]\( 3x^2 + 4x = 112 \)[/tex].
So, the correct answer is option A.
Let's break down the information:
1. We have two integers. Let's call one integer [tex]\( x \)[/tex].
2. According to the problem, the other integer is "four more than three times" the first integer. In mathematical terms, this can be expressed as [tex]\( 3x + 4 \)[/tex].
3. The product of these two integers is 112.
Now, let's formulate the equation:
- The product of the integers can be expressed as:
[tex]\[
x \times (3x + 4) = 112
\][/tex]
- Expanding the left side, we have:
[tex]\[
x \times (3x + 4) = 3x^2 + 4x
\][/tex]
- Therefore, the equation becomes:
[tex]\[
3x^2 + 4x = 112
\][/tex]
This matches option A, which is [tex]\( 3x^2 + 4x = 112 \)[/tex].
So, the correct answer is option A.
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