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The sum of two consecutive integers is 165. Choose the equation that can be solved to find the first of these two integers.

A. [tex]2x + 1 = 165[/tex]
B. [tex]2x = 165[/tex]
C. [tex]2x + 2 = 165[/tex]
D. [tex]4x + 2 = 165[/tex]
E. [tex]x + 1 = 165[/tex]

Answer :

To find the correct equation that represents the sum of two consecutive integers being 165, let's start solving this step-by-step:

1. Define Consecutive Integers:
- Let the first integer be [tex]\( x \)[/tex].
- The next consecutive integer would be [tex]\( x + 1 \)[/tex].

2. Set Up the Equation:
- According to the problem, the sum of these two integers is 165.
- This can be expressed as:
[tex]\[
x + (x + 1) = 165
\][/tex]

3. Simplify the Equation:
- Combine like terms:
[tex]\[
x + x + 1 = 165
\][/tex]
- Which simplifies to:
[tex]\[
2x + 1 = 165
\][/tex]

4. Choose the Correct Equation:
- From the options provided, the equation [tex]\( 2x + 1 = 165 \)[/tex] matches our derived equation.

Thus, the correct equation to find the first integer is [tex]\( 2x + 1 = 165 \)[/tex].

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