To solve this problem, we start by analyzing the equations provided in the options and solving them to find the second number, given that the first number is 10 and their sum is -18.
Option A:
The equation is [tex]\(10 - x = -18\)[/tex].
To solve for [tex]\(x\)[/tex], follow these steps:
1. Isolate [tex]\(x\)[/tex] by adding [tex]\(x\)[/tex] to both sides of the equation:
[tex]\[ 10 - x + x = -18 + x \][/tex]
This simplifies to:
[tex]\[ 10 = x - 18 \][/tex]
2. Next, isolate [tex]\(x\)[/tex] by subtracting 10 from both sides:
[tex]\[ 10 - 10 = x - 18 - 10 \][/tex]
This simplifies to:
[tex]\[ 0 = x - 28 \][/tex]
3. Finally, we need to isolate [tex]\(x\)[/tex] by adding 28 to both sides:
[tex]\[ 0 + 28 = x - 28 + 28 \][/tex]
This simplifies to:
[tex]\[ 28 = x \][/tex]
So, the second number is 28. Thus, Option A correctly represents the equation and solution.
Option B:
The equation is [tex]\(10 + x = -18\)[/tex].
To solve for [tex]\(x\)[/tex], follow these steps:
1. Subtract 10 from both sides of the equation:
[tex]\[ 10 + x - 10 = -18 - 10 \][/tex]
This simplifies to:
[tex]\[ x = -28 \][/tex]
So, the second number is -28. This doesn't match the correct solution.
Option C:
The equation is [tex]\(x - 10 = -18\)[/tex].
To solve for [tex]\(x\)[/tex], follow these steps:
1. Add 10 to both sides of the equation:
[tex]\[ x - 10 + 10 = -18 + 10 \][/tex]
This simplifies to:
[tex]\[ x = -8 \][/tex]
So, the second number is -8. This doesn't match the correct solution.
Option D:
The equation is [tex]\(-10 + x = -18\)[/tex].
To solve for [tex]\(x\)[/tex], follow these steps:
1. Add 10 to both sides of the equation:
[tex]\[ -10 + x + 10 = -18 + 10 \][/tex]
This simplifies to:
[tex]\[ x = -8 \][/tex]
So, the second number is -8. This doesn't match the correct solution.
Conclusion:
The correct option is A: The equation that represents this situation is [tex]\(10 - x = -18\)[/tex]. The second number is 28.
