Question

How do you solve and write the following in interval notation: `|2x-1|+7>=1`?

Answer 1

The solution set for `|2x-1|+7>=1` is `{x in RR}`

Explanation:

Subtract 7 from both sides

`|2x-1| >= -6`

The left hand side is always considered as positive. So it can not be equal to `-6` Thus `|2x-1|+7>=1` is wrong. It should read `|2x-1|+7>1`

The form of `|2x-1|+7>1` means that all real values of x will make the inequality be true.

The solution set for `|2x-1|+7>=1` is `{x in RR}`

To illustrate this, I shall substitute `1/2` for x:

`|2(1/2)-1|+7 >=1`

`|0|+ 7>=1`

`7 >=1`

This inequality is true and I have chosen the value for x where any other value will only make the number on the left side become greater. Therefore, the solution set is all real values of x.