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Answer :
To solve the problem of finding the equation that represents the statement "the sum of two consecutive integers is 143," let's break it down step-by-step:
1. Understand Consecutive Integers:
- Consecutive integers are numbers that follow each other in order, without any gaps. For example, if the first integer is represented by [tex]\( x \)[/tex], the next consecutive integer will be [tex]\( x + 1 \)[/tex].
2. Translate the Statement into an Equation:
- According to the statement, the sum of these two consecutive integers is 143. This means you need to add the two integers together and set that sum equal to 143.
3. Set up the Equation:
- The first integer is [tex]\( x \)[/tex].
- The next consecutive integer is [tex]\( x + 1 \)[/tex].
- Their sum can be expressed as: [tex]\( x + (x + 1) = 143 \)[/tex].
4. Simplify the Equation:
- Combine like terms: [tex]\( x + x + 1 = 143 \)[/tex] simplifies to [tex]\( 2x + 1 = 143 \)[/tex].
The equation that represents the statement is:
[tex]\[ x + (x + 1) = 143 \][/tex]
This equation correctly expresses that the sum of two consecutive integers equals 143, and you've derived it by following logical steps based on the problem statement.
1. Understand Consecutive Integers:
- Consecutive integers are numbers that follow each other in order, without any gaps. For example, if the first integer is represented by [tex]\( x \)[/tex], the next consecutive integer will be [tex]\( x + 1 \)[/tex].
2. Translate the Statement into an Equation:
- According to the statement, the sum of these two consecutive integers is 143. This means you need to add the two integers together and set that sum equal to 143.
3. Set up the Equation:
- The first integer is [tex]\( x \)[/tex].
- The next consecutive integer is [tex]\( x + 1 \)[/tex].
- Their sum can be expressed as: [tex]\( x + (x + 1) = 143 \)[/tex].
4. Simplify the Equation:
- Combine like terms: [tex]\( x + x + 1 = 143 \)[/tex] simplifies to [tex]\( 2x + 1 = 143 \)[/tex].
The equation that represents the statement is:
[tex]\[ x + (x + 1) = 143 \][/tex]
This equation correctly expresses that the sum of two consecutive integers equals 143, and you've derived it by following logical steps based on the problem statement.
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