Question

Can you help me with the question 4-5? Thank you.


((See below))

Answer 1

4)

`\bf 9x+4~~ \begin{cases} x=4(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(1)/(2)\\\\ 1(1)/(3)&x \end{array}\implies \cfrac{1}{~~1(1)/(3)~~}=\cfrac{~~6(1)/(2)~~}{x}\implies \stackrel{\textit{converting to \underline{improper}}}{\cfrac{~~1~~}{(4)/(3)}=\cfrac{(13)/(2)}{x}}\implies \cfrac{~~(1)/(1)~~}{(4)/(3)}=\cfrac{(13)/(2)}{(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(2)/(3)`