If I made a withdraw 3K from IRA and contributed 7k does 7k count towards the limit or 4k? Is there a 1 to 1 offset?

[Critter]

Contribution limits are not reduced by distributions.  And the deductible contributions and distributions are both entered on the return and do offset each other. 

[macuser_22]

Explain more.   What type of IRA - Roth of Traditional? 

Did you have $7,000 of taxable compensation to contribute?

Are you over age 50?

What exactally are you asking?

The most you can contribute to all of your traditional and Roth IRAs is the smaller of:

For 2018, $5,500, or $6,500 if you’re age 50 or older by the end of the year; or
your taxable compensation for the year.
For 2019, $6,000, or $7,000 if you’re age 50 or older by the end of the year; or
your taxable compensation for the year.

(Taxable compensation is generally wages that you worked for - W-2 or net self-employed income minus the deducible part of the SE tax, but can include commissions, alimony and separate maintenance, and nontaxable combat pay ).

See IRS Pub 590A "What is compensation" for details:
https://www.irs.gov/publications/p590a#en_US_2018_publink1000230355

See this IRS article for Roth contribution limits:

https://www.irs.gov/retirement-plans/roth-iras