Question

Solve the equation. Check your solution.$\mathbf{16}\mathbf{=}\mathbf{8}(\mathbf{x}\mathbf{-}\mathbf{1})$

Short answer

The solution for the equation $16=8(x-1)$is$x=3$ .

Step-by-step solution

Step 1. Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}16=8(x-1)\\ 16=8x-8\\ 16+8=8x-8+8\\ 24=8x\\ 8x=24\end{array}$

Step 2. Solve for x

Now, divide both sides of the equation by 3.

$\begin{array}{c}\frac{8x}{8}=\frac{24}{8}\\ x=3\end{array}$

Therefore, the solution of the equation is$x=3$.

Step 3. Check the solution 

To check the solution, write the original equation and substitute the value ofx.

$16=8\left(x-1\right)$

Now, substitute$x=3$ and check the result.

$\begin{array}{c}16=8(3-1)\\ 16=8\left(2\right)\\ 16=16\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.