Question

Which inequality is equivalent to |X-4| <9

a) -9>x-4<9

b) -9
c) x-4<-9 or -4<9

d) x-4>-9 or x-4<9

Answer 1

D. x-4>-9 or x-4<9

Explanation:

To solve this inequality, you have to isolate the term of x from one side of the equation.

|x-4|<9

-9<x-4<9

x-4>-9

First, add by 4 from both sides.

x-4+4>-9+4

Solve.

-9+4=-5

x>-5

x-4<9

Add by 4 from both sides.

x-4+4<9+4

Solve.

Add the numbers from left to right.

9+4=13

x<13

• Therefore, the correct answer is D. "x-4>-9 or x-4<9".

I hope this helps. Let me know if you have any questions.