For this case we have:
[tex]x + 7 \leq7[/tex]
If we subtract 7 on both sides we have:
[tex]x \leq7-7\\x \leq0[/tex]
The solution is given by all values of x less than or equal to 0.
On the other hand we have:
[tex]5 + 2x> 7[/tex]
Subtracting 5 from both sides:
[tex]2x> 7-5\\2x> 2[/tex]
Dividing between 2 on both sides we have:
[tex]x> \frac {2} {2}\\x> 1[/tex]
The solution is given by all the values of x higher than strict 1.
Finally the solution set is:
(-∞, 0] U (1, ∞)
Answer:
(-∞, 0] U (1, ∞)
