English question about correct word usage.

Difference between the sentences?

I am trying to figure out the difference between these sentences. When we use “having to” instead present participle, does it change the meaning of the sentence?

1a) I am bored to go to the office.
Vs
1b) I am bored having to go to the office.

2a) How to look pretty without having to wear makeup?
Vs
2b) How to look pretty without wearing makeup?

3a) You can sell arms without always having to use them.
Vs
3b) You can sell arms without always using them.

Can anyone help me with this?

Thanks in advance.