Question

If A-C-S, and AC =4x-1, AS = 6x-4, and CS=7, then find AC

Answer 1

`\underset{\leftarrow \qquad 6x - 4\qquad \to }{\stackrel{4x-1}{A\rule[0.35em]{17em}{0.25pt}C}\stackrel{7}{\rule[0.35em]{4em}{0.25pt}S}} \\\\\\ AC+CS=AS\implies (4x-1)+7=6x-4\implies 4x+6=6x-4 \\\\\\ 6=2x-4\implies 10=2x\implies \cfrac{10}{2}=x\implies \boxed{5=x} \\\\\\ \stackrel{AC}{4x-1}\implies 4(5)-1\implies 19`