Question

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

$x-\frac{1}{3}x-\frac{1}{2}x-5=0$

Short answer

The solution of the given equation is $x=30$.

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:

$x-\frac{1}{3}x-\frac{1}{2}x-5=0$

Step 3. Solve the given equation.

Simplify the given equation.

$\begin{array}{c}\left(1-\frac{1}{3}-\frac{1}{2}\right)x-5=0\\ \left(\frac{6-2-3}{6}\right)x-5=0\\ \frac{1}{6}x-5=0\end{array}$

Add$5$ on both sides.

role="math" localid="1643308797649" $\begin{array}{c}\frac{1}{6}x-5+5=0+5\\ \frac{1}{6}x=5\end{array}$

Multiply both sides by $6$.

$\begin{array}{c}6\times \frac{1}{6}x=6\times 5\\ x=30\end{array}$

Thus, the solution of the given equation is $x=30$.