To find the solution set for the inequalities and equations given:
-
Solve the inequality \( 2x > -8 \):
\[ x > \frac{-8}{2} \] \[ x > -4 \]
-
Solve the equation \( -5x + 7 = 12 \):
First, subtract 7 from both sides: \[ -5x = 12 - 7 \] \[ -5x = 5 \]
Next, divide both sides by -5: \[ x = \frac{5}{-5} \] \[ x = -1 \]
-
Combine the results:
- From the inequality, we have \( x > -4 \).
- From the equation, we have \( x = -1 \).
Since \(-1\) is greater than \(-4\), it satisfies the inequality \( 2x > -8 \).
- Conclusion:
The solution set is:
- The inequality \( x > -4 \) indicates all values greater than \(-4\).
- The equation \( x = -1 \) gives a specific solution.
Thus, the solution set combining both is:
- \( x = -1 \), which belongs to the solution set of the inequality \( x > -4 \).
In interval notation, the solution set can also be expressed as: \[ (-4, \infty) \text{ including the point } x = -1 \text{ which is a specific solution from the equation.} \]