Rewrite The Following Equation So That It Makes Sense:Given { X = \frac{4}{5} $}$, Solve The Equation { X + 10 $}$.
Understanding the Given Equation
The given equation is { x = \frac{4}{5} $}$, which represents a simple algebraic expression where x is equal to the fraction 4/5. However, the equation { x + 10 $}$ seems incomplete as it doesn't provide any information about the value of x. To rewrite the equation and make it solvable, we need to understand the context and the expected outcome.
Rewriting the Equation to Make Sense
To rewrite the equation { x + 10 $}$ and make it solvable, we need to substitute the given value of x into the equation. Since we know that { x = \frac{4}{5} $}$, we can substitute this value into the equation to get:
{ \frac{4}{5} + 10 $}$
Solving the Equation
To solve the equation { \frac{4}{5} + 10 $}$, we need to follow the order of operations (PEMDAS):
- Parentheses: None
- Exponents: None
- Multiplication and Division: None
- Addition and Subtraction: Perform the addition and subtraction operations from left to right
Step 1: Convert the Whole Number to a Fraction
To add the fraction { \frac{4}{5} $}$ and the whole number 10, we need to convert the whole number to a fraction with the same denominator. Since the denominator of the fraction is 5, we can convert the whole number 10 to a fraction with the denominator 5:
{ 10 = \frac{50}{5} $}$
Step 2: Add the Fractions
Now that we have the fraction { \frac{50}{5} $}$ and the fraction { \frac{4}{5} $}$, we can add them together:
{ \frac{50}{5} + \frac{4}{5} = \frac{54}{5} $}$
Step 3: Simplify the Result
The result of the addition is the fraction { \frac{54}{5} $}$. This fraction cannot be simplified further, so the final answer is:
{ x + 10 = \frac{54}{5} $}$
Conclusion
In conclusion, to rewrite the given equation { x + 10 $}$ and make it solvable, we need to substitute the given value of x into the equation. By substituting { x = \frac4}{5} $}$ into the equation, we get { \frac{4}{5} + 10 $}$. By following the order of operations and converting the whole number to a fraction, we can add the fractions together to get the final answer{5} $}$.
Example Use Case
This problem can be used as an example in a mathematics textbook or online resource to demonstrate how to rewrite and solve algebraic equations. It can also be used as a practice problem for students to test their understanding of algebraic expressions and equations.
Real-World Application
This problem has real-world applications in various fields such as finance, engineering, and science. For example, in finance, this problem can be used to calculate the total cost of an item after adding a fixed amount. In engineering, this problem can be used to calculate the total distance traveled by an object after adding a fixed distance. In science, this problem can be used to calculate the total amount of a substance after adding a fixed amount.
Future Research Directions
Future research directions in this area can include:
- Developing new methods for rewriting and solving algebraic equations
- Investigating the applications of algebraic equations in various fields
- Developing new tools and resources for teaching and learning algebraic equations
Limitations of the Current Study
The current study has several limitations, including:
- The study only focuses on a simple algebraic equation
- The study does not investigate the applications of algebraic equations in various fields
- The study does not develop new methods for rewriting and solving algebraic equations
Future Studies
Future studies can build on the current study by:
- Investigating the applications of algebraic equations in various fields
- Developing new methods for rewriting and solving algebraic equations
- Developing new tools and resources for teaching and learning algebraic equations
Conclusion
In conclusion, this study demonstrates how to rewrite and solve a simple algebraic equation. The study provides a step-by-step solution to the equation and highlights the importance of following the order of operations. The study also discusses the real-world applications of algebraic equations and suggests future research directions.
Understanding Algebraic Equations
Algebraic equations are mathematical expressions that contain variables and constants. They are used to represent relationships between variables and can be solved to find the value of the variable. In the previous article, we discussed how to rewrite and solve a simple algebraic equation. In this article, we will answer some frequently asked questions about solving algebraic equations.
Q: What is an algebraic equation?
A: An algebraic equation is a mathematical expression that contains variables and constants. It is used to represent relationships between variables and can be solved to find the value of the variable.
Q: How do I solve an algebraic equation?
A: To solve an algebraic equation, you need to follow the order of operations (PEMDAS):
- Parentheses: Evaluate expressions inside parentheses
- Exponents: Evaluate any exponential expressions
- Multiplication and Division: Evaluate any multiplication and division operations from left to right
- Addition and Subtraction: Evaluate any addition and subtraction operations from left to right
Q: What is the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction
Q: How do I evaluate expressions inside parentheses?
A: To evaluate expressions inside parentheses, you need to follow the order of operations (PEMDAS) inside the parentheses. For example, if you have the expression (2 + 3) * 4, you would first evaluate the expression inside the parentheses (2 + 3) to get 5, and then multiply 5 by 4 to get 20.
Q: How do I evaluate exponential expressions?
A: To evaluate exponential expressions, you need to raise the base number to the power of the exponent. For example, if you have the expression 2^3, you would raise 2 to the power of 3 to get 8.
Q: How do I evaluate multiplication and division operations?
A: To evaluate multiplication and division operations, you need to perform the operations from left to right. For example, if you have the expression 12 ÷ 3 * 2, you would first divide 12 by 3 to get 4, and then multiply 4 by 2 to get 8.
Q: How do I evaluate addition and subtraction operations?
A: To evaluate addition and subtraction operations, you need to perform the operations from left to right. For example, if you have the expression 5 + 2 - 3, you would first add 5 and 2 to get 7, and then subtract 3 from 7 to get 4.
Q: What is the difference between a variable and a constant?
A: A variable is a symbol that represents a value that can change. A constant is a value that does not change.
Q: How do I solve an equation with multiple variables?
A: To solve an equation with multiple variables, you need to isolate one variable at a time. You can do this by using algebraic manipulations such as addition, subtraction, multiplication, and division.
Q: What is the purpose of solving algebraic equations?
A: The purpose of solving algebraic equations is to find the value of the variable. Algebraic equations are used to represent relationships between variables and can be solved to find the value of the variable.
Q: How do I apply algebraic equations in real-life situations?
A: Algebraic equations can be applied in various real-life situations such as finance, engineering, and science. For example, in finance, algebraic equations can be used to calculate the total cost of an item after adding a fixed amount. In engineering, algebraic equations can be used to calculate the total distance traveled by an object after adding a fixed distance.
Conclusion
In conclusion, solving algebraic equations is an important skill that can be applied in various real-life situations. By following the order of operations (PEMDAS) and using algebraic manipulations, you can solve algebraic equations and find the value of the variable.