Question

give me questions similar to |x+11|=24 and the sum of the solutions to the given equation

Answer 1

Sure! Here are some similar equations in the same form as \(|x + 11| = 24\):

1. \(|x - 5| = 10\)
2. \(|x + 7| = 15\)
3. \(|2x + 3| = 9\)
4. \(|x - 12| = 6\)
5. \(|3x + 4| = 12\)

Now, let’s find the sum of the solutions to the original equation \(|x + 11| = 24\):

To solve \(|x + 11| = 24\), we need to consider two cases:

1. \(x + 11 = 24\)
- Solving for \(x\):
\[
x = 24 - 11 = 13
\]

2. \(x + 11 = -24\)
- Solving for \(x\):
\[
x = -24 - 11 = -35
\]

Now we have the two solutions: \(x = 13\) and \(x = -35\).

To find the sum of the solutions:
\[
13 + (-35) = 13 - 35 = -22
\]

Thus, the sum of the solutions to \(|x + 11| = 24\) is \(-22\).

Let me know if you'd like to calculate the solutions and their sum for any of the new equations!