# Show steps on how to solve this equation: 9x -12 = 78

## Question:

Show steps on how to solve this equation:

9x -12 = 78

## Transposition in Algebra

Terms are expressions that are separated by addition or subtraction. When rearranging terms that stays on one side of the equation, always bring the sign of the term with it. When rearranging terms that crosses over the equation, the sign is left behind and changes sign.

In solving for {eq}x {/eq} in the algebraic equation below:

{eq}9x -12 = 78 {/eq}

In order to remove the {eq}-12 {/eq} on the left hand side of the equal sign you need add {eq}12 {/eq}. But then the right side would no longer be equal to it. So you also need to add {eq}12 {/eq} to the right side. A good rule to remember is when you do one thing to one side of an equation, you have to do the same on the other so that the equation would stay equal. Thus, the equation would look like:

{eq}9x -12 +12 = 78 +12 {/eq}

{eq}9x = 78 +12 {/eq}

{eq}9x = 90 {/eq}

To remove the coefficient of {eq}x {/eq} we divide both sides by the coefficient {eq}9 {/eq}:

{eq}\displaystyle \frac{9x}{9} = \frac{90}{9} {/eq}

{eq}\displaystyle x = 10 {/eq}

To check, we substitute it in the equation:

{eq}9x -12 = 78 {/eq}

{eq}9(10) -12 \stackrel{?}{=} 78 {/eq}

{eq}90 -12 \stackrel{?}{=} 78 {/eq}

{eq}78 \stackrel{\checkmark}{=} 78 {/eq}

Therefore, the value of {eq}x {/eq} from {eq}9x -12 = 78 {/eq} is {eq}10 {/eq}. 