# How do you solve  8x-1=63?

Jun 19, 2018

$x = 8$

#### Explanation:

$\text{isolate "8x" by adding 1 to both sides of the equation}$

$8 x = 63 + 1 = 64$

$\text{divide both sides by 8}$

$\frac{\cancel{8} x}{\cancel{8}} = \frac{64}{8} \Rightarrow x = 8$

$\textcolor{b l u e}{\text{As a check}}$

$\left(8 \times 8\right) - 1 = 64 - 1 = 63 \leftarrow \text{correct}$

Jun 19, 2018

x = 8

#### Explanation:

$8 x = 63 + 1$
$8 x = 64$
$x = \frac{64}{8}$
$x = 8$

Jun 19, 2018

Using Addition/Subtraction, 'move' all the constants to one side of the equation, and then divide through by $x$'s coefficient to find $x = 8$

#### Explanation:

Our goal is to get $x$ by itself. We will do this by applying factors to both sides of the equation.

The first step is to get all constants to the opposite side of the equation as $x$. For this scenario, that means eliminating the '-1' from the left hand side (LHS) and doing the same operation to the right hand side (RHS). How will we eliminate the '-1'? By adding 1 to both sides. This preserves equality for both sides.

$8 x - 1 \textcolor{red}{+ 1} = 63 \textcolor{red}{+ 1}$

$8 x \textcolor{red}{+ 0} = 63 \textcolor{red}{+ 1}$

$8 x = 64$

Next, we need to eliminate $x$'s coefficient. You would normally do this by multiplying or dividing both sides of the equation. For our purposes, the coefficient is 8, so we will divide both sides by 8 to determine what $x$ is equal to:

$\frac{8 x}{\textcolor{red}{8}} = \frac{64}{\textcolor{red}{8}}$

$\frac{8}{\textcolor{red}{8}} x = \frac{64}{\textcolor{red}{8}}$

$\textcolor{red}{1} x = \frac{64}{\textcolor{red}{8}}$

$\textcolor{g r e e n}{x = 8}$