Are they a system or separate inequalities? I'm not sure but either way I will solve each:
[tex]\begin{bmatrix}-3x+5>20\\ \frac{1}{2}x-12<6\end{bmatrix}[/tex]
[tex]-3x+5>20,\\-3x>15,\\x<-5[/tex]
[tex]\frac{1}{2}x-12<6,\\\frac{1}{2}x<18,\\x<36[/tex]
Now if it were a system, the solution would be x<-5, since x<36 is the restriction. Otherwise just take x<-5 and x<36 independent of each other.
Answer:
x< -5, x<36
Step-by-step explanation:
[tex]-3x+5>20} \atop {\frac{1}{2}x-12<6 }} \right. \\[/tex]
Start with the first equation and solve for x
-3x+5>20
-5 -5
-3x>15
/-3 /-3
x< -5
Do the second:
[tex]\frac{1}{2}x-12<6[/tex]
+12 +12
[tex]\frac{1}{2}x[/tex]<18
/0.5 /0.5
x< 36
