Question

Can you help me with the question 4-5? Thank you. ((See below))

Answer 1

4)

$\bf 9x+4~~ \begin{cases} x=4\frac{1}{3}\\\\ \qquad \cfrac{4\cdot 3+1}{3}\\\\ \qquad \cfrac{13}{3} \end{cases}\implies 9\left( \cfrac{13}{3} \right)+4\implies \cfrac{117}{3}+4 \\\\\\ \stackrel{\textit{using }\stackrel{LCD}{3}}{\cfrac{(1)117+(3)4}{3}}\implies \cfrac{117+12}{3}\implies \cfrac{129}{3}\implies 43$

5)

$\bf \begin{array}{ccll} bag&lbs\\ \cline{1-2} 1&6\frac{1}{2}\\\\ 1\frac{1}{3}&x \end{array}\implies \cfrac{1}{~~1\frac{1}{3}~~}=\cfrac{~~6\frac{1}{2}~~}{x}\implies \stackrel{\textit{converting to \underline{improper}}}{\cfrac{~~1~~}{\frac{4}{3}}=\cfrac{\frac{13}{2}}{x}}\implies \cfrac{~~\frac{1}{1}~~}{\frac{4}{3}}=\cfrac{\frac{13}{2}}{\frac{x}{1}}$

$\bf \cfrac{1}{1}\cdot \cfrac{3}{4}=\cfrac{13}{2}\cdot \cfrac{1}{x}\implies \cfrac{3}{4}=\cfrac{13}{2x}\implies 6x=52\implies x=\cfrac{52}{6}\implies x=8\frac{2}{3}$