Answer :
To solve the problem of finding the equation that represents the sum of two consecutive odd numbers, we first need to understand what consecutive odd numbers are.
Consecutive odd numbers follow one after another. If we take the first odd number to be represented as [tex]\(2x + 1\)[/tex] (because any odd number can be expressed in the form of [tex]\(2x + 1\)[/tex] where [tex]\(x\)[/tex] is an integer), then the next consecutive odd number would be two units more, which is [tex]\(2x + 3\)[/tex].
Now, we need to find the sum of these two consecutive odd numbers:
- The first odd number: [tex]\(2x + 1\)[/tex]
- The second consecutive odd number: [tex]\(2x + 3\)[/tex]
The sum of these two numbers is:
[tex]\((2x + 1) + (2x + 3)\)[/tex]
According to the problem, the sum is equal to 124. So, the equation we need to solve is:
[tex]\((2x + 1) + (2x + 3) = 124\)[/tex]
Now let's check the given options to find the correct one:
- a. [tex]\(2x + 1 = 124\)[/tex]: This represents only one number, not the sum of two.
- b. [tex]\(2x + x = 124\)[/tex]: This doesn’t represent the consecutive odd numbers properly.
- c. [tex]\((2x + 1) + (2x + 3) = 124\)[/tex]: This correctly represents the sum of the consecutive odd numbers.
- d. [tex]\(x + (x+1) = 124\)[/tex]: This represents the sum of two consecutive numbers, not consecutive odd numbers.
Thus, the correct equation is option c: [tex]\((2x + 1) + (2x + 3) = 124\)[/tex].
Consecutive odd numbers follow one after another. If we take the first odd number to be represented as [tex]\(2x + 1\)[/tex] (because any odd number can be expressed in the form of [tex]\(2x + 1\)[/tex] where [tex]\(x\)[/tex] is an integer), then the next consecutive odd number would be two units more, which is [tex]\(2x + 3\)[/tex].
Now, we need to find the sum of these two consecutive odd numbers:
- The first odd number: [tex]\(2x + 1\)[/tex]
- The second consecutive odd number: [tex]\(2x + 3\)[/tex]
The sum of these two numbers is:
[tex]\((2x + 1) + (2x + 3)\)[/tex]
According to the problem, the sum is equal to 124. So, the equation we need to solve is:
[tex]\((2x + 1) + (2x + 3) = 124\)[/tex]
Now let's check the given options to find the correct one:
- a. [tex]\(2x + 1 = 124\)[/tex]: This represents only one number, not the sum of two.
- b. [tex]\(2x + x = 124\)[/tex]: This doesn’t represent the consecutive odd numbers properly.
- c. [tex]\((2x + 1) + (2x + 3) = 124\)[/tex]: This correctly represents the sum of the consecutive odd numbers.
- d. [tex]\(x + (x+1) = 124\)[/tex]: This represents the sum of two consecutive numbers, not consecutive odd numbers.
Thus, the correct equation is option c: [tex]\((2x + 1) + (2x + 3) = 124\)[/tex].
