Question

Geometry homework, I understood 5 and 6 but I'm kinda lost on 7 and 8. Can someone please explain them to me?

Answer 1

ab and bc are congruent. ac is ab+bc. So, bc is 2ab or 2bc.
In 7 and 8, you have ab and ac. So, solve for x by equating 2ab to ac. The rest should be easy for you!
7:
2(x+6)=3x-31
2x+12=3x-31
x=43
8:
2(3(3x-1))=5(2x+2)
18x-6=10x+10
8x=16
x=2

Answer 2

$\bf \underset{\leftarrow \qquad 3x - 31\qquad \to }{\boxed{A}\stackrel{x+6}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{x + 6}{\rule[0.35em]{10em}{0.25pt}}\boxed{C}} \\\\\\ (x+6)+(x+6) = 3x - 31\implies 2x+12=3x-31 \\\\\\ 12=x-31\implies 43=x \\\\[-0.35em] ~\dotfill\\\\ AB\implies BC\implies x+6\implies 43+6\implies 49 \\\\\\ AC\implies AB+BC\implies 49+49\implies 98$