Question

Find the value of the variable.

$3u+\left(u-2\right)=10$

Short answer

The value of the variable is $\mathit{u}\mathbf{=}\mathbf{3}$.

Step-by-step solution

Step 1. Combine the like terms.

First remove all the brackets and combine the like terms 3u and u.

$\begin{array}{l}3u+\left(u-2\right)=10\\ 3u+u-2=10\\ 4u-2=10\end{array}$

Step 2. Add 2.

To find the value of variable u in the equation $4u-2=10$, add 2 on both sides of the equation.

$\begin{array}{l}4u-2+2=10+2\\ 4u=12\end{array}$

Step 3. Divide by 4.

Divide both sides of the equation$4u=12$ by 4 and cancel the common factors of 4 on both sides.

$\begin{array}{l}\frac{4u}{4}=\frac{12}{4}\\ u=\frac{4\times 3}{4}\\ u=3\end{array}$

Step 4. Verify the value.

In order to verify the value of u, substitute 3 for u into the equation $3u+\left(u-2\right)=10$.

$\begin{array}{l}3\times 3+\left(3-2\right)=10\\ 9+1=10\\ 10=10\text{True}\end{array}$

Hence, the value of the variable is $u=3$.