Question

1/3 (x + 5) + x = 4 ( x - 4) -9

Answer 1

$\frac{1}{3}(x+5)+x=4(x-4)-9$

Distributing and combining similar terms

$\begin{gathered} \frac{1}{3}\cdot x+\frac{1}{3}\cdot5+x=4\cdot x-4\cdot4-9 \\ \frac{1}{3}x+x+\frac{5}{3}=4x-16-9 \\ \frac{4}{3}x+\frac{5}{3}=4x-25 \end{gathered}$

Subtracting 4/3x at both sides

$\begin{gathered} \frac{4}{3}x+\frac{5}{3}-\frac{4}{3}x=4x-25-\frac{4}{3}x \\ \frac{5}{3}=(4-\frac{4}{3})x-25 \\ \frac{5}{3}=(\frac{4\cdot3-4}{3})x-25 \\ \frac{5}{3}=\frac{8}{3}x-25 \end{gathered}$

Adding 25 at both sides:

$\begin{gathered} \frac{5}{3}+25=\frac{8}{3}x-25+25 \\ \frac{5+25\cdot3}{3}=\frac{8}{3}x \\ \frac{80}{3}=\frac{8}{3}x \end{gathered}$

Multiplying by 3/8 at both sides

$\begin{gathered} \frac{80}{3}\cdot\frac{3}{8}=\frac{8}{3}x\cdot\frac{3}{8} \\ \frac{80}{8}=x \\ 10=x \end{gathered}$