Answer:
x < -1 or x > 9
Step-by-step explanation:
[tex]10|x-4|-3>47[/tex]
Add 3 to both sides.
[tex]10|x-4|-3+3>47+3[/tex]
Simplify.
[tex]10|x-4|>50[/tex]
Divide both sides by 10.
[tex]\frac{10|x-4|}{10} >\frac{50}{10}[/tex]
Simplify.
[tex]|x-4|>5[/tex]
Apply absolute value rule: If [tex]|u|>a,a>0[/tex] then [tex]u < -a[/tex] or [tex]u>a[/tex]
[tex]x-4<5[/tex] or [tex]x-4 >5[/tex]
[tex]x-4<-5[/tex]
Add 4 to both sides.
[tex]x-4+4<-5+4[/tex]
Simplify.
[tex]x<-1[/tex]
[tex]x-4>5[/tex]
Add 4 to both sides.
[tex]x-4+4>5+4[/tex]
Simplify.
[tex]x>9[/tex]
Combine the intervals.
[tex]x<-1[/tex] or [tex]x>9[/tex]
