Question
Solve: $\frac{3 x-2}{3}+\frac{2 x+3}{2}=x+\frac{7}{6}$
✓
Answer
$ \frac{3 x-2}{3}+\frac{2 x+3}{2}=x+\frac{7}{6}$
$ \Rightarrow \frac{2(3 x-2)+3(2 x+3)}{6}=x+\frac{7}{6}$
$ \Rightarrow \frac{6 x-4+6 x+9}{6}=\frac{6 x+7}{6}$
$ \Rightarrow \frac{12 x+5}{6}=\frac{6 x+7}{6}$
$ \Rightarrow 6(12 x+5)=6(6 x+7)$
$ \Rightarrow 72 x+30=36 x-42$
$ \Rightarrow 72 x-36 x=42-30$
$ \Rightarrow 36 x=12$
$ x=\frac{12}{36}$
$ \therefore \frac{1}{3}$
$ \Rightarrow \frac{2(3 x-2)+3(2 x+3)}{6}=x+\frac{7}{6}$
$ \Rightarrow \frac{6 x-4+6 x+9}{6}=\frac{6 x+7}{6}$
$ \Rightarrow \frac{12 x+5}{6}=\frac{6 x+7}{6}$
$ \Rightarrow 6(12 x+5)=6(6 x+7)$
$ \Rightarrow 72 x+30=36 x-42$
$ \Rightarrow 72 x-36 x=42-30$
$ \Rightarrow 36 x=12$
$ x=\frac{12}{36}$
$ \therefore \frac{1}{3}$
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