Question

Find the value of the variable.

$x+9x=5$

Short answer

The value of the variable is $\mathit{x}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}$.

Step-by-step solution

Step 1. Combine the like terms.

To simplify combine the like terms x and 9x.

$\begin{array}{l}x+9x=5\\ 10x=5\end{array}$

Step 2. Divide by 10.

To find the value of variable x in the equation $10x=5$, divide both sides of the equation by 10.

$\frac{10x}{10}=\frac{5}{10}$

Step 3. Simplify the equation.

To further simplify, cancel the common factors of 10 on both sides.

$\begin{array}{l}\frac{10x}{10}=\frac{5}{5\times 2}\\ x=\frac{1}{2}\end{array}$

Step 4. Verify the value.

In order to verify the value of x, substitute $\frac{1}{2}$ for x into the equation $x+9x=5$.

$\begin{array}{l}\frac{1}{2}+9\times \frac{1}{2}=5\\ \frac{10}{2}=5\\ 5=5\text{True}\end{array}$

Hence, the value of the variable is $x=\frac{1}{2}$.