Question

I just need these 2 questions answered (the second pic is just confirmation i'm not confident in that answer)

Answer 1

Read the explanation. The paragraphs are for each question.

Explanation:

If a - 7 is positive, we will get a - 7
`\leq` 5, and when a - 7 is negative, we get 7 - a
`\leq` 5, and we can multiply both sides by -1 and we also need to switch the sign (you can figure this out by adding and subtracting things), so we get a - 7
`\geq` -5. This means the answer is the 2nd choice, as we do not need them both to be satisfied.

For the 2nd part, we do the same thing. We have
`3 + |t+4|<10 \implies |t+4|<7.` Now, we have the same two cases, and we get either
`t<3`, or
`-t-4<7`, and we multiply by -1 again to get
`t+4>-7 \implies t>-11`. So, we get
`-11<t<3` as our answer.