The first inequality has solution
.. 5x +7 > -8
.. 5x > -15 . . . . subtract 7
.. x > -3 . . . . . . divide by 5
The second inequality has solution
.. 3x +7 ≤ 19
.. 3x ≤ 12 . . . . . subtract 7
.. x ≤ 4 . . . . . . . divide by 3
The solution to the compound inequality is
.. -3 < x ≤ 4