Answer:
[tex]x\in (-\infty,-24)\cup [6,\infty)[/tex]
Step-by-step explanation:
The given compound inequality is
[tex]\frac{1}{8}x-5<-8[/tex] or [tex]7x-4\geq 38[/tex]
Solve each inequality.
On solving first inequality we get
[tex]\frac{1}{8}x-5<-8[/tex]
Add 5 on both sides.
[tex]\frac{1}{8}x-5+5<-8+5[/tex]
[tex]\frac{1}{8}x<-3[/tex]
Multiply both sides by 8.
[tex]x<-24[/tex] .... (1)
On solving second inequality we get
[tex]7x-4\geq 38[/tex]
Add 4 on both sides.
[tex]7x\geq 42[/tex]
Divide both sides by 7.
[tex]x\geq 6[/tex] .... (2)
Using (1) and (2) the value of x is either less than -24 or greater than or equal to 6.
[tex]x\in(-\infty,-24)\cup [6,\infty)[/tex]
