Question

The heights of tomato plants exhibited on a farmer's trade show satisfied the equation \(\dfrac{x+1}{1+2 x}=\dfrac{1}{3}\). Find the value of \(x\).

Answer 1

\[
\frac{2 x+1}{1+2 x}=\frac{1}{3}
\]
Then \(3(2 x-1)=1(1+2 x)\) (by cross multiplication')
\[
6 x-3=1+2 x
\]
And \(6 x-2 x=1+3\) (subtracting \(2 x\) and 3 from both sides)
\[
\begin{aligned}
&4x=4 \\
&\frac{4 x}{x}=\frac{4}{4} \\
&x=1
\end{aligned}
\]