Answer :
To solve the problem of finding the equation that represents "the sum of two consecutive integers is 143," let's break it down step-by-step:
1. Understanding consecutive integers:
- Consecutive integers are numbers that follow one another in order. For example, 5 and 6 are consecutive integers.
- If we let [tex]\( x \)[/tex] be an integer, then the next consecutive integer would be [tex]\( x + 1 \)[/tex].
2. Sum of two consecutive integers:
- According to the problem, the sum of these two consecutive integers is 143.
- So, we can write this as: [tex]\( x + (x + 1) = 143 \)[/tex].
3. Formulating the equation:
- Simplify the left-hand side of the equation: [tex]\( x + (x + 1) \)[/tex] becomes [tex]\( 2x + 1 \)[/tex].
- Therefore, the equation is [tex]\( 2x + 1 = 143 \)[/tex].
So, the correct equation from the given options that represents "the sum of two consecutive integers is 143" is:
[tex]\[
x + (x + 1) = 143
\][/tex]
This matches with the option:
[tex]\[
x + x + 1 = 143
\][/tex]
To confirm the solution step by step:
4. Solving the equation:
- We start with [tex]\( 2x + 1 = 143 \)[/tex].
- Subtract 1 from both sides to isolate the term with [tex]\( x \)[/tex]: [tex]\( 2x = 142 \)[/tex].
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]: [tex]\( x = 71 \)[/tex].
5. Verification:
- The consecutive integers are 71 and 72.
- Sum of 71 and 72 is [tex]\( 71 + 72 = 143 \)[/tex], which is correct.
Thus, the original equation [tex]\( x + x + 1 = 143 \)[/tex] correctly represents the problem statement, and the integers 71 and 72 satisfy the equation.
So, the correct answer is:
[tex]\[
x + x + 1 = 143
\][/tex]
1. Understanding consecutive integers:
- Consecutive integers are numbers that follow one another in order. For example, 5 and 6 are consecutive integers.
- If we let [tex]\( x \)[/tex] be an integer, then the next consecutive integer would be [tex]\( x + 1 \)[/tex].
2. Sum of two consecutive integers:
- According to the problem, the sum of these two consecutive integers is 143.
- So, we can write this as: [tex]\( x + (x + 1) = 143 \)[/tex].
3. Formulating the equation:
- Simplify the left-hand side of the equation: [tex]\( x + (x + 1) \)[/tex] becomes [tex]\( 2x + 1 \)[/tex].
- Therefore, the equation is [tex]\( 2x + 1 = 143 \)[/tex].
So, the correct equation from the given options that represents "the sum of two consecutive integers is 143" is:
[tex]\[
x + (x + 1) = 143
\][/tex]
This matches with the option:
[tex]\[
x + x + 1 = 143
\][/tex]
To confirm the solution step by step:
4. Solving the equation:
- We start with [tex]\( 2x + 1 = 143 \)[/tex].
- Subtract 1 from both sides to isolate the term with [tex]\( x \)[/tex]: [tex]\( 2x = 142 \)[/tex].
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]: [tex]\( x = 71 \)[/tex].
5. Verification:
- The consecutive integers are 71 and 72.
- Sum of 71 and 72 is [tex]\( 71 + 72 = 143 \)[/tex], which is correct.
Thus, the original equation [tex]\( x + x + 1 = 143 \)[/tex] correctly represents the problem statement, and the integers 71 and 72 satisfy the equation.
So, the correct answer is:
[tex]\[
x + x + 1 = 143
\][/tex]
