Respuesta :

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]

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