Question

The solution to equation is$3 \frac{(x - 6)}{5} = x$

Answer 1

Solution of an equation

Initial explanation

We want to find which value must have x, so this equations is true:

$\frac{3(x-6)}{5}=x$

In order to solve the equation for x we want to "leave it alone" on one side of the equation.

In order to do that we just have to remember one simple rule:

Step by step

Step 1: simplifying the expression with parenthesis

We use the distributive property to "take off" the parenthesis of the left side:

$\begin{gathered} \frac{3(x-6)}{5}=x \\ \downarrow \\ \frac{3x-3\cdot6}{5}=\frac{3x-18}{5} \\ \downarrow \\ \frac{3x-18}{5}=x \end{gathered}$

Step 2: simplifying the fraction

We take the denominator of the left to the right side:

$\begin{gathered} \frac{3x-18}{5}=x \\ \downarrow \\ 5\cdot\frac{3x-18}{5}=5\cdot x \\ \downarrow \\ 3x-18=5x \end{gathered}$

Step 3: taking all the terms with x to the right side

We take 3x to the right side:

$\begin{gathered} 3x-18=5x \\ \downarrow \\ -3x+3x-18=-3x+5x \\ \downarrow\text{ since -3x + 3x = 0 and -3x + 5x = 2x} \\ 0-18=2x \\ \downarrow \\ -18=2x \end{gathered}$

Step 4: "leaving x alone"

We take 2 to the left side:

$\begin{gathered} -18=2x \\ \downarrow \\ -\frac{18}{2}=\frac{2x}{2} \\ \downarrow\text{ since -18/2=9 and 2x/2=x} \\ -9=x \end{gathered}$

Answer: x = -9