How Can $x-\frac{2}{3}=\frac{5}{6}$ Be Solved For $x$ In One Step?A. Add $\frac{2}{3}$ To Both Sides.B. Add $ 5 6 \frac{5}{6} 6 5 ​ [/tex] To Both Sides.C. Subtract $\frac{2}{3}$ From Both Sides.D.

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific type of linear equation, namely $x-\frac{2}{3}=\frac{5}{6}$, in one step. We will explore the different methods of solving this equation and provide a step-by-step guide on how to arrive at the solution.

Understanding the Equation

The given equation is $x-\frac2}{3}=\frac{5}{6}$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. The equation consists of two terms $x$ and $-\frac{2{3}$. Our goal is to get rid of the $-\frac{2}{3}$ term and isolate $x$.

Method 1: Adding $\frac{2}{3}$ to Both Sides

One way to solve the equation is to add $\frac{2}{3}$ to both sides of the equation. This will eliminate the $-\frac{2}{3}$ term and allow us to isolate $x$.

x - \frac{2}{3} = \frac{5}{6}
x - \frac{2}{3} + \frac{2}{3} = \frac{5}{6} + \frac{2}{3}
x = \frac{5}{6} + \frac{2}{3}

To add $\frac{2}{3}$ to $\frac{5}{6}$, we need to find a common denominator, which is 6. We can rewrite $\frac{2}{3}$ as $\frac{4}{6}$.

x = \frac{5}{6} + \frac{4}{6}
x = \frac{9}{6}
x = \frac{3}{2}

Method 2: Subtracting $\frac{2}{3}$ from Both Sides

Another way to solve the equation is to subtract $\frac{2}{3}$ from both sides of the equation. This will also eliminate the $-\frac{2}{3}$ term and allow us to isolate $x$.

x - \frac{2}{3} = \frac{5}{6}
x - \frac{2}{3} - \frac{2}{3} = \frac{5}{6} - \frac{2}{3}
x = \frac{5}{6} - \frac{4}{6}
x = \frac{1}{6}

Method 3: Adding $\frac{5}{6}$ to Both Sides

We can also solve the equation by adding $\frac{5}{6}$ to both sides of the equation. This will eliminate the $-\frac{2}{3}$ term and allow us to isolate $x$.

x - \frac{2}{3} = \frac{5}{6}
x - \frac{2}{3} + \frac{5}{6} = \frac{5}{6} + \frac{5}{6}
x = \frac{10}{6}
x = \frac{5}{3}

Conclusion

In this article, we have explored three different methods of solving the linear equation $x-\frac{2}{3}=\frac{5}{6}$ in one step. We have shown that adding $\frac{2}{3}$ to both sides, subtracting $\frac{2}{3}$ from both sides, and adding $\frac{5}{6}$ to both sides are all valid methods of solving the equation. The solution to the equation is $x = \frac{3}{2}$, $x = \frac{1}{6}$, and $x = \frac{5}{3}$, respectively.

Final Answer

The final answer to the equation $x-\frac{2}{3}=\frac{5}{6}$ is: