Question

Rewrite the given inequality as two linear inequalities. ∣8x+9∣<4

Answer 1

`8x+9<4` and
`8x+9>-4`.

Explanation:

The given inequality is

`|8x+9|<4`

We need to rewrite the given inequality as two linear inequalities.

We know that |8x+9|>0 but (8x+9) can be positive or negative.

For
`|8x+9|<4`, the value of (8x+9) must be lies between -4 and 4.

i.e.,
`-4<8x+9<4`

If 8x+9 positive, then

`8x+9<4` ...(1)

If 8x+9 negative, then

`8x+9>-4` ...(2)

Therefore, the two inequalities are
`8x+9<4` and
`8x+9>-4`.