Solve For \[$ X \$\].$\[ X = \square \\]$\[ \frac{44}{x} = \frac{5}{7} \\]

Introduction to Solving Equations

Solving equations is a fundamental concept in mathematics that involves finding the value of a variable that makes an equation true. In this article, we will focus on solving a specific type of equation, where the variable is isolated on one side of the equation. We will use the given equation $\frac{44}{x} = \frac{5}{7}$ as an example to demonstrate the steps involved in solving for $x$.

Understanding the Equation

The given equation is a rational equation, which means it contains fractions. The equation is $\frac{44}{x} = \frac{5}{7}$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. The first step is to cross-multiply, which involves multiplying both sides of the equation by the denominators of the fractions.

Cross-Multiplying

Cross-multiplying is a technique used to eliminate the fractions in a rational equation. To cross-multiply, we multiply both sides of the equation by the denominators of the fractions. In this case, we multiply both sides by $x$ and $7$. This gives us:

$$44 \cdot 7 = 5 \cdot x$$

Simplifying the Equation

After cross-multiplying, we simplify the equation by multiplying the numbers on the left-hand side. This gives us:

$$308 = 5x$$

Isolating the Variable

Now that we have simplified the equation, we need to isolate the variable $x$ on one side of the equation. To do this, we divide both sides of the equation by $5$. This gives us:

$$x = \frac{308}{5}$$

Evaluating the Expression

To find the value of $x$, we need to evaluate the expression $\frac{308}{5}$. This involves dividing $308$ by $5$.

Calculating the Value of $x$

To calculate the value of $x$, we perform the division:

$$x = \frac{308}{5} = 61.6$$

Conclusion

In this article, we solved the equation $\frac{44}{x} = \frac{5}{7}$ for $x$. We used the technique of cross-multiplying to eliminate the fractions and then isolated the variable $x$ on one side of the equation. Finally, we evaluated the expression to find the value of $x$. The value of $x$ is $61.6$.

Tips and Tricks

• When solving rational equations, it's essential to cross-multiply to eliminate the fractions.
• Make sure to simplify the equation after cross-multiplying.
• Isolate the variable on one side of the equation by performing the necessary operations.
• Evaluate the expression to find the value of the variable.

Common Mistakes to Avoid

• Failing to cross-multiply when solving rational equations.
• Not simplifying the equation after cross-multiplying.
• Not isolating the variable on one side of the equation.
• Not evaluating the expression to find the value of the variable.

Real-World Applications

Solving equations is a fundamental concept in mathematics that has numerous real-world applications. Some examples include:

• Physics: Solving equations is used to describe the motion of objects and to calculate quantities such as velocity and acceleration.
• Engineering: Solving equations is used to design and optimize systems, such as bridges and buildings.
• Economics: Solving equations is used to model economic systems and to make predictions about future trends.

Final Thoughts

Solving equations is a critical skill in mathematics that has numerous real-world applications. By following the steps outlined in this article, you can solve equations and find the value of variables. Remember to cross-multiply, simplify the equation, isolate the variable, and evaluate the expression to find the value of the variable. With practice and patience, you can become proficient in solving equations and apply this skill to real-world problems.