Determine the solution set of 2x>−8 and −5x+7=12.(1 point)
A. {−1}
left brace negative 1 right brace
B. {−4}
left brace negative 4 right brace
C. {x|x>−4}
left brace x vertical bar x greater than negative 4 right brace
D. {x|x>−1}
The solution set is D. {x|x>−1}.
To determine the solution set of the given inequalities, we need to solve both equations separately.
Starting with the first equation:
2x > -8
Divide both sides of the inequality by 2:
x > -4
Now, let's move on to the second equation:
-5x + 7 = 12
Subtract 7 from both sides of the equation:
-5x = 5
Divide both sides of the equation by -5 (note that when dividing by a negative number, the inequality sign must be reversed):
x < -1
Therefore, the solution set consists of values of x that satisfy both inequalities:
x > -4 (from the first inequality)
and
x < -1 (from the second inequality)
Combining these two constraints, we find the solution set:
{x|x > -4 and x < -1}
Simplifying this interval notation gives us:
{x|-4 < x < -1}
Therefore, the correct answer is option C: {x|x > -4}.