Question

What is the solution of 9|2x – 1| + 4 < 49?

Answer 1

see explanation

Explanation:

Given

9 | 2x - 1 | + 4 < 49 ( subtract 4 from both sides )

9 | 2x - 1 | < 45 ( divide both sides by 9 )

| 2x - 1 | < 5

Inequalities of the type | x | < a always have solutions of the form

- a < x < a, thus

- 5 < 2x - 1 < 5 ( add 1 to all 3 intervals )

- 4 < 2x < 6 ( divide all 3 intervals by 2 )

- 2 < x < 3

Answer 2

Answer:
`-2<x<3`

Explanation:

You need to set up two cases (Positive case and negative case) and solve for "x".

- POSITIVE CASE IF:
`2x-1>0`

`9(2x -1) + 4 < 49\\18x-9<49-4\\18x<54\\x<3`

- NEGATIVE CASE IF:
`2x-1<0`

`-9(2x -1) + 4 < 49\\-18x+9<49-4\\-18x<36\\x>-2`

Therefore, the solution is:

`-2<x<3`