Question

Solve the equation and check the solution.

$3x+6=22$

Short answer

The solution is $x=\frac{16}{3}$.

Step-by-step solution

Step 1- Consider the equation.

Consider the equation $3x+6=22$.

Subtract 22 from both sides of the equation.

Step 2- Step description.

$\begin{array}{c}3x+6-22=0\\ 3x-16=0\end{array}$

Step 3- Step description.

Add 16 on both sides of the equation as follows:

$\begin{array}{c}3x-16=0\\ 3x-16+16=16\\ 3x=16\end{array}$

Divide both sides of the equation by 3.

$\begin{array}{l}3x=16\\ x=\frac{16}{3}\end{array}$

Therefore, the solution is $x=\frac{16}{3}$.

Step 4- Verify the solution.

Substitute $x=\frac{16}{3}$in the equation and simplify as follows:

$\begin{array}{c}3x+6=22\\ 3\left(\frac{16}{3}\right)+6=22\\ 16+6=22\\ 22=22\end{array}$

Since the left-hand side of the equation is equal to the right-hand side of the equation, therefore, the solution is $x=\frac{16}{3}$.