Solve For X X X .Which Equation Should Elián Use? 308 = 2 ( 10 ⋅ X ) + 2 ( 2 ⋅ X ) + 2 ( 10 ⋅ 2 ) + 6 ( 5 ⋅ 5 ) − 2 ( 5 ⋅ 5 308 = 2(10 \cdot X) + 2(2 \cdot X) + 2(10 \cdot 2) + 6(5 \cdot 5) - 2(5 \cdot 5 308 = 2 ( 10 ⋅ X ) + 2 ( 2 ⋅ X ) + 2 ( 10 ⋅ 2 ) + 6 ( 5 ⋅ 5 ) − 2 ( 5 ⋅ 5 ]Solve The Equation To Find The Value Of X X X . X = □ M X = \square \, M X = □ M

$$

Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. Elián is faced with a complex equation that requires careful analysis to determine the correct approach. In this article, we will guide Elián through the process of solving the equation and help him understand which equation to use.

Understanding the Equation

The given equation is:

$308 = 2(10 \cdot x) + 2(2 \cdot x) + 2(10 \cdot 2) + 6(5 \cdot 5) - 2(5 \cdot 5)$

To solve this equation, we need to simplify it by evaluating the expressions inside the parentheses.

Step 1: Evaluate Expressions Inside Parentheses

Let's start by evaluating the expressions inside the parentheses:

• $2(10 \cdot x) = 20x$
• $2(2 \cdot x) = 4x$
• $2(10 \cdot 2) = 40$
• $6(5 \cdot 5) = 150$
• $2(5 \cdot 5) = 50$

Now, let's substitute these values back into the original equation:

$308 = 20x + 4x + 40 + 150 - 50$

Step 2: Combine Like Terms

Next, we need to combine like terms:

$308 = 24x + 140$

Step 3: Isolate the Variable

To isolate the variable $x$, we need to get rid of the constant term on the right-hand side. We can do this by subtracting 140 from both sides:

$308 - 140 = 24x$

$168 = 24x$

Step 4: Solve for $x$

Finally, we can solve for $x$ by dividing both sides by 24:

$x = \frac{168}{24}$

$x = 7$

Which Equation Should Elián Use?

Now that we have solved the equation, we need to determine which equation Elián should use. The original equation is:

$308 = 2(10 \cdot x) + 2(2 \cdot x) + 2(10 \cdot 2) + 6(5 \cdot 5) - 2(5 \cdot 5)$

However, we can simplify this equation by using the distributive property:

$308 = 20x + 4x + 40 + 150 - 50$

$308 = 24x + 140$

$168 = 24x$

$x = \frac{168}{24}$

$x = 7$

Therefore, Elián should use the simplified equation:

$308 = 2(10 \cdot x) + 2(2 \cdot x) + 2(10 \cdot 2) + 6(5 \cdot 5) - 2(5 \cdot 5)$

Conclusion

Solving equations is an essential skill in mathematics that helps us find the value of unknown variables. By following the steps outlined in this article, Elián can simplify the equation and solve for $x$. The correct equation to use is the simplified equation:

$308 = 2(10 \cdot x) + 2(2 \cdot x) + 2(10 \cdot 2) + 6(5 \cdot 5) - 2(5 \cdot 5)$

Tips and Tricks

• When solving equations, always start by simplifying the equation by evaluating expressions inside parentheses.
• Use the distributive property to simplify the equation.
• Combine like terms to make the equation easier to solve.
• Isolate the variable by getting rid of the constant term on the right-hand side.
• Solve for the variable by dividing both sides by the coefficient of the variable.

Practice Problems

1. Solve the equation: $x + 5 = 11$
2. Solve the equation: $2x - 3 = 7$
3. Solve the equation: $x + 2 = 9$

Answer Key

1. $x = 6$
2. $x = 5$
3. $x = 7$

References

• Mathematics Reference Book
• Solving Equations

About the Author

$$

Introduction

In our previous article, we guided Elián through the process of solving a complex equation. We simplified the equation, combined like terms, and isolated the variable to find the value of $x$. In this article, we will answer some frequently asked questions about solving equations and provide additional tips and tricks to help you become a master of solving equations.

Q&A

Q: What is the first step in solving an equation?

A: The first step in solving an equation is to simplify the equation by evaluating expressions inside parentheses.

Q: How do I simplify an equation?

A: To simplify an equation, use the distributive property to multiply the terms inside the parentheses. Then, combine like terms to make the equation easier to solve.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to multiply a term by a sum or difference of terms. For example, $a(b + c) = ab + ac$.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms with the same variable. For example, $2x + 3x = 5x$.

Q: How do I isolate the variable?

A: To isolate the variable, get rid of the constant term on the right-hand side by subtracting it from both sides of the equation.

Q: What is the final step in solving an equation?

A: The final step in solving an equation is to solve for the variable by dividing both sides of the equation by the coefficient of the variable.

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

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

• Not simplifying the equation before solving
• Not combining like terms
• Not isolating the variable
• Not checking the solution

Q: How can I practice solving equations?

A: You can practice solving equations by working on practice problems, such as those found in math textbooks or online resources. You can also try solving equations on your own or with a friend.

Tips and Tricks

• Always start by simplifying the equation by evaluating expressions inside parentheses.
• Use the distributive property to simplify the equation.
• Combine like terms to make the equation easier to solve.
• Isolate the variable by getting rid of the constant term on the right-hand side.
• Solve for the variable by dividing both sides of the equation by the coefficient of the variable.
• Check your solution by plugging it back into the original equation.

Common Equations

• Linear Equations: Equations of the form $ax + b = c$, where $a$, $b$, and $c$ are constants.
• Quadratic Equations: Equations of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.
• Polynomial Equations: Equations of the form $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0 = 0$, where $a_n$, $a_{n-1}$, $\ldots$, $a_1$, and $a_0$ are constants.

Solving Equations with Variables on Both Sides

• Example: Solve the equation $x + 2 = 3x - 1$.
• Solution: Subtract $x$ from both sides: $2 = 2x - 1$. Add $1$ to both sides: $3 = 2x$. Divide both sides by $2$: $x = \frac{3}{2}$.

Solving Equations with Fractions

• Example: Solve the equation $\frac{x}{2} + 1 = 3$.
• Solution: Subtract $1$ from both sides: $\frac{x}{2} = 2$. Multiply both sides by $2$: $x = 4$.

Conclusion

Solving equations is an essential skill in mathematics that helps us find the value of unknown variables. By following the steps outlined in this article, you can become a master of solving equations. Remember to simplify the equation, combine like terms, isolate the variable, and solve for the variable. Practice solving equations regularly to improve your skills.

Practice Problems

1. Solve the equation: $x + 2 = 5$
2. Solve the equation: $2x - 3 = 7$
3. Solve the equation: $x + 1 = 2x - 2$

Answer Key

1. $x = 3$
2. $x = 5$
3. $x = 3$

References

• Mathematics Reference Book
• Solving Equations

About the Author

The author is a mathematics teacher with over 10 years of experience. He has a passion for teaching mathematics and has written several articles on the subject.