Answer :
To solve the problem, we have to represent the statement "the sum of two consecutive integers is 143" using an equation. Here's the step-by-step process:
1. Understand the Terminology:
- Consecutive integers are numbers that follow each other in order. For example, if you have one integer `x`, the next consecutive integer would be `x + 1` because it is one greater than `x`.
2. Set up the Variables:
- Let's call the first integer `x`.
- Then, the next consecutive integer is `x + 1`.
3. Translate the Sentence into an Equation:
- The problem states that the sum of these two integers is 143.
- Therefore, we set up the equation as:
[tex]\[
x + (x + 1) = 143
\][/tex]
4. Simplify the Equation:
- Combine like terms: [tex]\(x + x + 1\)[/tex] becomes [tex]\(2x + 1\)[/tex].
- So the equation can be rewritten as:
[tex]\[
2x + 1 = 143
\][/tex]
5. Solve the Equation (Optional if required):
- Subtract 1 from both sides to isolate terms with [tex]\(x\)[/tex]:
[tex]\[
2x = 142
\][/tex]
- Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 71
\][/tex]
- The second consecutive integer is [tex]\(x + 1\)[/tex], which equals 72.
Thus, two consecutive integers that sum to 143 are 71 and 72, but the required equation in this problem is [tex]\( x + (x + 1) = 143 \)[/tex].
1. Understand the Terminology:
- Consecutive integers are numbers that follow each other in order. For example, if you have one integer `x`, the next consecutive integer would be `x + 1` because it is one greater than `x`.
2. Set up the Variables:
- Let's call the first integer `x`.
- Then, the next consecutive integer is `x + 1`.
3. Translate the Sentence into an Equation:
- The problem states that the sum of these two integers is 143.
- Therefore, we set up the equation as:
[tex]\[
x + (x + 1) = 143
\][/tex]
4. Simplify the Equation:
- Combine like terms: [tex]\(x + x + 1\)[/tex] becomes [tex]\(2x + 1\)[/tex].
- So the equation can be rewritten as:
[tex]\[
2x + 1 = 143
\][/tex]
5. Solve the Equation (Optional if required):
- Subtract 1 from both sides to isolate terms with [tex]\(x\)[/tex]:
[tex]\[
2x = 142
\][/tex]
- Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 71
\][/tex]
- The second consecutive integer is [tex]\(x + 1\)[/tex], which equals 72.
Thus, two consecutive integers that sum to 143 are 71 and 72, but the required equation in this problem is [tex]\( x + (x + 1) = 143 \)[/tex].
