To solve the given inequalities and equations, we can break them down step-by-step.
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Solve the inequality: \(2x > -8\)
To isolate \(x\), divide both sides by 2:
\[ x > -4 \]
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Solve the equation: \(-5x + 7 = 12\)
First, subtract 7 from both sides:
\[ -5x = 12 - 7 \]
\[ -5x = 5 \]
Next, divide both sides by -5 (remember that dividing by a negative number flips the inequality):
\[ x = -1 \]
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Combine the results
We have:
- From the inequality \(2x > -8\), we found \(x > -4\).
- From the equation \(-5x + 7 = 12\), we found \(x = -1\).
Now, let's determine if \(x = -1\) satisfies the inequality \(x > -4\):
Since \(-1 > -4\) is true, it is part of the solution set.
Thus, the solution set consists of the point from the equation and the inequality limits:
The solution set is:
\[ { x = -1 } \text{ for } 2x > -8 \] or more generally, expressed with respect to the inequality:
\[ x \in (-4, \infty) \text{ includes } x = -1 \]
The complete solution set includes \(x = -1\) as it satisfies both the inequality and the equation.