Answer :
To solve the problem of finding the first number from the given equation [tex]\(2n + 1 = 157\)[/tex], follow these steps:
1. Understand the Equation: The equation represents the sum of two consecutive numbers. The first number is [tex]\(n\)[/tex], and the second number is [tex]\(n + 1\)[/tex]. Hence, the sum of these two numbers is [tex]\(n + (n + 1)\)[/tex], which simplifies to [tex]\(2n + 1\)[/tex].
2. Set the Equation: You have [tex]\(2n + 1 = 157\)[/tex].
3. Isolate the [tex]\(2n\)[/tex] Term:
- Subtract 1 from both sides of the equation to isolate the term involving [tex]\(n\)[/tex]:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
- Simplify the equation:
[tex]\[
2n = 156
\][/tex]
4. Solve for [tex]\(n\)[/tex]:
- Divide both sides by 2 to solve for [tex]\(n\)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
- Calculate the result:
[tex]\[
n = 78
\][/tex]
Therefore, the first number is 78. So, the correct answer is B. 78.
1. Understand the Equation: The equation represents the sum of two consecutive numbers. The first number is [tex]\(n\)[/tex], and the second number is [tex]\(n + 1\)[/tex]. Hence, the sum of these two numbers is [tex]\(n + (n + 1)\)[/tex], which simplifies to [tex]\(2n + 1\)[/tex].
2. Set the Equation: You have [tex]\(2n + 1 = 157\)[/tex].
3. Isolate the [tex]\(2n\)[/tex] Term:
- Subtract 1 from both sides of the equation to isolate the term involving [tex]\(n\)[/tex]:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
- Simplify the equation:
[tex]\[
2n = 156
\][/tex]
4. Solve for [tex]\(n\)[/tex]:
- Divide both sides by 2 to solve for [tex]\(n\)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
- Calculate the result:
[tex]\[
n = 78
\][/tex]
Therefore, the first number is 78. So, the correct answer is B. 78.
