Find the range of values of x for which 3x - 7 ≤ 0 and x + 5 > 0
Answer Details
To solve this inequality, we need to work with each inequality separately and then find the values of x that satisfy both.
Starting with the first inequality:
3x - 7 ≤ 0
Adding 7 to both sides:
3x ≤ 7
Dividing by 3:
x ≤ 7/3
Now, let's work with the second inequality:
x + 5 > 0
Subtracting 5 from both sides:
x > -5
To satisfy both inequalities, x must be greater than -5 and less than or equal to 7/3. Therefore, the range of values for x is:
-5 < x ≤ 7/3