Solve The Equation: 5 X 2 = 18 \frac{5x}{2} = 18 2 5 X ​ = 18

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Introduction

Mathematics is a fundamental subject that deals with numbers, quantities, and shapes. It is a crucial tool for problem-solving and critical thinking. In mathematics, equations play a vital role in representing relationships between variables. Solving equations is an essential skill that helps us understand the world around us. In this article, we will focus on solving a simple equation: $\frac{5x}{2} = 18$. We will use step-by-step instructions and provide examples to help readers understand the concept.

Understanding the Equation

The given equation is $\frac{5x}{2} = 18$. This equation represents a relationship between the variable $x$ and the constant $18$. The equation states that the product of $5$ and $x$ divided by $2$ is equal to $18$. To solve for $x$, we need to isolate the variable on one side of the equation.

Step 1: Multiply Both Sides by 2

To eliminate the fraction, we can multiply both sides of the equation by $2$. This will help us get rid of the denominator. The equation becomes:

$$5x = 36$$

Step 2: Divide Both Sides by 5

Now that we have eliminated the fraction, we can divide both sides of the equation by $5$. This will help us isolate the variable $x$. The equation becomes:

$$x = \frac{36}{5}$$

Step 3: Simplify the Expression

The expression $\frac{36}{5}$ can be simplified by dividing $36$ by $5$. This will give us the value of $x$.

$$x = 7.2$$

Conclusion

In this article, we have solved the equation $\frac{5x}{2} = 18$ using step-by-step instructions. We have multiplied both sides of the equation by $2$ to eliminate the fraction, and then divided both sides by $5$ to isolate the variable $x$. The final answer is $x = 7.2$. This equation represents a simple relationship between the variable $x$ and the constant $18$. Solving equations like this one helps us develop problem-solving skills and critical thinking.

Real-World Applications

Solving equations like $\frac{5x}{2} = 18$ has many real-world applications. For example, in finance, equations like this one can be used to calculate interest rates or investment returns. In science, equations like this one can be used to model population growth or chemical reactions. In engineering, equations like this one can be used to design bridges or buildings.

Tips and Tricks

• When solving equations, always start by isolating the variable on one side of the equation.
• Use inverse operations to eliminate fractions or decimals.
• Check your work by plugging the solution back into the original equation.

Common Mistakes

• Forgetting to multiply or divide both sides of the equation by the same value.
• Not checking the solution by plugging it back into the original equation.
• Not using inverse operations to eliminate fractions or decimals.

Conclusion

Solving equations like $\frac{5x}{2} = 18$ is an essential skill that helps us understand the world around us. By following step-by-step instructions and using inverse operations, we can solve equations like this one and develop problem-solving skills and critical thinking. Remember to always check your work and use inverse operations to eliminate fractions or decimals.

Final Answer

The final answer is $x = 7.2$.

Introduction

Solving equations is a fundamental concept in mathematics that helps us understand the world around us. In our previous article, we solved the equation $\frac{5x}{2} = 18$ using step-by-step instructions. In this article, we will answer some frequently asked questions about solving equations.

Q: What is an equation?

A: An equation is a statement that two expressions are equal. It is a mathematical statement that represents a relationship between variables and constants.

Q: What is the difference between an equation and an expression?

A: An expression is a group of numbers, variables, and mathematical operations that are combined to form a value. An equation, on the other hand, is a statement that two expressions are equal.

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the variable on one side of the equation. You can do this by using inverse operations, such as addition and subtraction, multiplication and division.

Q: What is an inverse operation?

A: An inverse operation is a mathematical operation that undoes the effect of another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I use inverse operations to solve an equation?

A: To use inverse operations to solve an equation, you need to identify the operation that is being performed on the variable. Then, you need to perform the inverse operation to isolate the variable.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my work when solving an equation?

A: To check your work when solving an equation, you need to plug the solution back into the original equation. If the solution is true, then you have solved the equation correctly.

Q: What are some common mistakes to avoid when solving equations?

A: Some common mistakes to avoid when solving equations include:

• Forgetting to multiply or divide both sides of the equation by the same value.
• Not checking the solution by plugging it back into the original equation.
• Not using inverse operations to eliminate fractions or decimals.

Q: How do I solve equations with fractions or decimals?

A: To solve equations with fractions or decimals, you need to use inverse operations to eliminate the fraction or decimal. For example, if you have the equation $\frac{x}{2} = 3$, you can multiply both sides of the equation by $2$ to eliminate the fraction.

Q: How do I solve equations with variables on both sides?

A: To solve equations with variables on both sides, you need to use inverse operations to eliminate the variable on one side of the equation. For example, if you have the equation $x + 2 = 5$, you can subtract $2$ from both sides of the equation to eliminate the variable on the right side.

Conclusion

Solving equations is a fundamental concept in mathematics that helps us understand the world around us. By following the steps outlined in this article, you can solve equations with confidence and develop problem-solving skills and critical thinking. Remember to always check your work and use inverse operations to eliminate fractions or decimals.

Final Answer

The final answer is that solving equations is a crucial skill that helps us understand the world around us. By following the steps outlined in this article, you can solve equations with confidence and develop problem-solving skills and critical thinking.