Question

The given equation is either linear or equivalent to a linear equation. Solve the equation.

$\frac{1}{x}=\frac{4}{3x}+1$

Short answer

The solution of the given equation is $x=-\frac{1}{3}$.

Step-by-step solution

Step 1. Definition of equation.

Equation is a mathematical statement in which two expressions are equal to each other.

Step 2. Given Information.

The given equation is:

$\frac{1}{x}=\frac{4}{3x}+1$

Step 3. Solve the given equation.

LCM of$x$ and$3x$ is $3x$, so multiply both sides by$3x$ to simplify the given equation.

role="math" localid="1643310689225" $$\begin{gathered} 3x\left(\frac{1}{x}\right)=3x\left(\frac{4}{3x}+1\right) \\ 3=3x\left(\frac{4}{3x}\right)+3x\left(1\right) \\ 3=4+3x \end{gathered}$$

Subtract$4$ from both sides.

role="math" localid="1643310432720" $$\begin{gathered} 3-4=4+3x-4 \\ -1=3x \end{gathered}$$

Divide both sides by $3$.

role="math" localid="1643310524019" $$\begin{gathered} \frac{-1}{3}=\frac{3x}{3} \\ -\frac{1}{3}=x \end{gathered}$$

Thus, the solution of the given equation is $x=-\frac{1}{3}$.