Solve For $x$: $\frac{2x}{14} = 7$x =$ $\square$

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Introduction to Solving Equations

Solving equations is a fundamental concept in mathematics that involves isolating the variable of interest. In this case, we are given the equation $\frac{2x}{14} = 7$ and we need to solve for the value of $x$. This equation is a simple algebraic equation that can be solved using basic algebraic manipulations.

Understanding the Equation

The given equation is $\frac{2x}{14} = 7$. This equation states that the ratio of $2x$ to $14$ is equal to $7$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation.

Isolating the Variable

To isolate the variable $x$, we can start by multiplying both sides of the equation by $14$. This will eliminate the fraction and allow us to work with a simpler equation.

Multiplying Both Sides by 14

$\frac{2x}{14} \times 14 = 7 \times 14$

This simplifies to:

$2x = 98$

Solving for $x$

Now that we have the equation $2x = 98$, we can solve for $x$ by dividing both sides of the equation by $2$.

Dividing Both Sides by 2

$2x \div 2 = 98 \div 2$

This simplifies to:

$x = 49$

Conclusion

In this article, we solved the equation $\frac{2x}{14} = 7$ for the value of $x$. We started by multiplying both sides of the equation by $14$ to eliminate the fraction, and then we divided both sides of the equation by $2$ to isolate the variable $x$. The final solution is $x = 49$.

Tips and Tricks for Solving Equations

• Always start by simplifying the equation and eliminating any fractions or decimals.
• Use basic algebraic manipulations such as multiplying or dividing both sides of the equation to isolate the variable.
• Be careful when dividing both sides of the equation by a variable, as this can result in an incorrect solution.

Common Mistakes to Avoid

• Failing to simplify the equation before solving for the variable.
• Not isolating the variable on one side of the equation.
• Dividing both sides of the equation by a variable without checking if the variable is equal to zero.

Real-World Applications of Solving Equations

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

• Calculating the cost of goods and services
• Determining the amount of time it takes to complete a task
• Finding the area and perimeter of shapes
• Solving problems in physics and engineering

Final Thoughts

Solving equations is a critical skill that is used in many areas of mathematics and science. By following the steps outlined in this article, you can solve equations with confidence and accuracy. Remember to always simplify the equation, isolate the variable, and be careful when dividing both sides of the equation by a variable. With practice and patience, you can become proficient in solving equations and apply this skill to real-world problems.

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Introduction to Solving Equations Q&A

In our previous article, we solved the equation $\frac{2x}{14} = 7$ for the value of $x$. In this article, we will answer some frequently asked questions about solving equations.

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

A: The first step in solving an equation is to simplify the equation and eliminate any fractions or decimals. This will make it easier to isolate the variable.

Q: How do I eliminate fractions in an equation?

A: To eliminate fractions in an equation, you can multiply both sides of the equation by the denominator of the fraction. For example, if the equation is $\frac{2x}{14} = 7$, you can multiply both sides by $14$ to eliminate the fraction.

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

A: An equation is a statement that says two things are equal, while an expression is a group of numbers and variables that are combined using mathematical operations. For example, $2x + 3$ is an expression, while $2x + 3 = 5$ is an equation.

Q: How do I solve an equation with a variable on both sides?

A: To solve an equation with a variable on both sides, you can add or subtract the same value to both sides of the equation to isolate the variable. For example, if the equation is $x + 2 = 5$, you can subtract $2$ from both sides to get $x = 3$.

Q: What is the order of operations in solving an equation?

A: The order of operations in solving an equation is:

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

Q: How do I check my solution to an equation?

A: To check your solution to an equation, you can plug the solution back into the original equation and see if it is true. For example, if the equation is $x + 2 = 5$ and you think the solution is $x = 3$, you can plug $x = 3$ back into the equation and see if it is true.

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

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

• Failing to simplify the equation before solving for the variable.
• Not isolating the variable on one side of the equation.
• Dividing both sides of the equation by a variable without checking if the variable is equal to zero.
• Not checking the solution to the equation.

Q: How do I apply solving equations to real-world problems?

A: Solving equations can be applied to many real-world problems, such as:

• Calculating the cost of goods and services
• Determining the amount of time it takes to complete a task
• Finding the area and perimeter of shapes
• Solving problems in physics and engineering

Conclusion

Solving equations is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article, you can solve equations with confidence and accuracy. Remember to always simplify the equation, isolate the variable, and be careful when dividing both sides of the equation by a variable. With practice and patience, you can become proficient in solving equations and apply this skill to real-world problems.