Question

determine the solution set of 2x>-8 and -5x +7 =12

Answer 1

so is it this {-1} or this {x|x>-1}

Answer 2

To determine the solution set for the given inequalities and equations, we'll solve each one step-by-step.

### For the inequality \(2x > -8\):

1. Divide both sides by 2:
\[
x > -4
\]

### For the equation \(-5x + 7 = 12\):

1. Subtract 7 from both sides:
\[
-5x = 12 - 7
\]
\[
-5x = 5
\]

2. Divide both sides by \(-5\) (note that this reverses the inequality):
\[
x = -1
\]

### Solution Set:

Now we compare the results of both parts:

- From the inequality, we have \( x > -4 \).
- From the equation, we have \( x = -1 \).

Since \(-1\) is greater than \(-4\), it satisfies the inequality.

### Conclusion:

The solution set is:
- For the inequality: \(x > -4\)
- The solution to the equation: \(x = -1\)

Thus, \(x = -1\) is a valid solution in the context of the inequality, and both the inequality and equation can be satisfied with this value of \(x\).

The complete solution set is:
\[
\{ x \mid x > -4 \} \text{ and } x = -1
\]
Thus, while the solution to the equation is \(x = -1\), it also falls within the solution set of the inequality.

Answer 3

Thank you for your question! Let's clarify the solution set based on what we've discussed.

1. **From the inequality** \(2x > -8\):
- The solution is \(x > -4\).

2. **From the equation** \(-5x + 7 = 12\):
- The solution is \(x = -1\).

### Conclusion

- The solution to the equation is a single value: \(\{-1\}\).
- The solution to the inequality is a range of values: \(\{x \mid x > -4\}\).

If we want to summarize both findings:

- The value \(-1\) satisfies both the equation and falls within the range given by the inequality.
- However, \(-1\) is not related to \(x > -1\); rather, it is related to \(x > -4\).

Thus, the solutions are:

- **For the equation**: \(\{-1\}\)
- **For the inequality**: \(\{x \mid x > -4\}\)

So, in totality, the stated solution set for the equation is \(\{-1\}\), while for the inequality, it is \(\{x \mid x > -4\}\).

If you are asking whether to combine the two into a single answer—it would depend on the context. If you just need the solutions separately, they remain distinct as explained above.