Answer:
Read the explanation. The paragraphs are for each question.
Step-by-step explanation:
If a - 7 is positive, we will get a - 7 [tex]\leq[/tex] 5, and when a - 7 is negative, we get 7 - a [tex]\leq[/tex] 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 [tex]\geq[/tex] -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 [tex]3 + |t+4|<10 \implies |t+4|<7.[/tex] Now, we have the same two cases, and we get either [tex]t<3[/tex], or [tex]-t-4<7[/tex], and we multiply by -1 again to get [tex]t+4>-7 \implies t>-11[/tex]. So, we get [tex]-11<t<3[/tex] as our answer.
