Solve the following equation. x/11=x/12-9

Question:

Solve the following equation.

{eq}\frac{x}{11}=\frac{x}{12}-9 {/eq}

Solving Simple Algebraic Equations:

A simple algebraic equation is an equation that contains only one variable. Such an equation requires the basic principals of equality to solve for the unknown in the equation.

Answer and Explanation:


We have the equation:

$$\begin{align} \dfrac{x}{11}=\dfrac{x}{12}-9 \end{align} $$

In the above equation, the LCM of the denominator is {eq}132 {/eq}. Multiplying both sides of the equation by the LCM,we get:

$$\begin{align} \dfrac{x}{11}\times 132&=\left(\dfrac{x}{12}-9\right)\times 132\\[0.3cm] 12x&=11x-1188 \end{align} $$

Subtracting {eq}11x {/eq} from both sides of the equation, we get:

$$\begin{align} 12x-11x&=-1188\\[0.3cm] x&=\boxed{\color{blue}{-1188}} \end{align} $$


Learn more about this topic:

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Common Algebraic Equations: Linear, Quadratic, Polynomial, and More

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Chapter 8 / Lesson 9
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Watch this video lesson to see the kinds of equations that you will come across most often in algebra. Learn to distinguish them by just looking for the identifying components of each equation.


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