Solve For $f$:$8 = F - (13 - 2)$ Be Sure To Show Your Work.

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Understanding the Problem

The given equation is a simple algebraic expression that requires us to solve for the variable $f$. The equation is $8 = f - (13 - 2)$, and our goal is to isolate the variable $f$ and find its value.

Step 1: Simplify the Expression Inside the Parentheses

The first step in solving this equation is to simplify the expression inside the parentheses. We have $13 - 2$ inside the parentheses, which can be simplified as follows:

13−2=1113 - 2 = 11

So, the equation becomes:

8=f−118 = f - 11

Step 2: Add 11 to Both Sides of the Equation

To isolate the variable $f$, we need to get rid of the negative term $-11$ that is being subtracted from $f$. We can do this by adding $11$ to both sides of the equation. This will cancel out the $-11$ term and leave us with just $f$ on one side of the equation.

8+11=f−11+118 + 11 = f - 11 + 11

Simplifying the left-hand side of the equation, we get:

19=f19 = f

Step 3: Write the Final Answer

We have now solved for the variable $f$ and found its value to be $19$. Therefore, the final answer to the equation $8 = f - (13 - 2)$ is:

f=19f = 19

Conclusion

In this article, we solved for the variable $f$ in the equation $8 = f - (13 - 2)$. We simplified the expression inside the parentheses, added $11$ to both sides of the equation, and finally isolated the variable $f$ to find its value. The final answer to the equation is $f = 19$.

Frequently Asked Questions

  • Q: What is the value of $f$ in the equation $8 = f - (13 - 2)$?
  • A: The value of $f$ is $19$.
  • Q: How do I simplify the expression inside the parentheses in the equation?
  • A: To simplify the expression inside the parentheses, you need to perform the arithmetic operation inside the parentheses first. In this case, we simplified $13 - 2$ to $11$.
  • Q: How do I isolate the variable $f$ in the equation?
  • A: To isolate the variable $f$, you need to get rid of the negative term that is being subtracted from $f$. You can do this by adding the same value to both sides of the equation.

Tips and Tricks

  • When solving algebraic equations, it's essential to follow the order of operations (PEMDAS) to simplify the expression inside the parentheses.
  • To isolate the variable, you need to get rid of the negative term that is being subtracted from the variable.
  • When adding or subtracting the same value to both sides of the equation, make sure to simplify the left-hand side of the equation to get the final answer.

Related Topics

  • Algebraic equations
  • Simplifying expressions
  • Isolating variables
  • Order of operations (PEMDAS)

Further Reading

  • For more information on algebraic equations, check out our article on "Solving Linear Equations".
  • For more information on simplifying expressions, check out our article on "Simplifying Algebraic Expressions".
  • For more information on isolating variables, check out our article on "Isolating Variables in Algebraic Equations".

Frequently Asked Questions

Algebraic Equations

  • Q: What is an algebraic equation?
    • A: An algebraic equation is a mathematical statement that contains variables and constants, and is used to solve for the value of the variable.
  • Q: How do I solve an algebraic equation?
    • A: To solve an algebraic equation, you need to isolate the variable by getting rid of the constants and other variables.
  • 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 simplifying an expression. The acronym PEMDAS stands for:
      • Parentheses: Evaluate expressions inside parentheses first.
      • Exponents: Evaluate any exponential expressions next.
      • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
      • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
  • Q: How do I simplify an algebraic expression?
    • A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary parentheses.

Simplifying Expressions

  • Q: What is a like term?
    • A: A like term is a term that has the same variable and exponent as another term.
  • Q: How do I combine like terms?
    • A: To combine like terms, you need to add or subtract the coefficients of the like terms.
  • Q: What is a coefficient?
    • A: A coefficient is a number that is multiplied by a variable.
  • Q: How do I eliminate unnecessary parentheses?
    • A: To eliminate unnecessary parentheses, you need to simplify the expression inside the parentheses first.

Isolating Variables

  • Q: What is a variable?
    • A: A variable is a letter or symbol that represents a value that can change.
  • Q: How do I isolate a variable?
    • A: To isolate a variable, you need to get rid of the constants and other variables that are being added or subtracted from the variable.
  • Q: What is the difference between adding and subtracting the same value to both sides of an equation?
    • A: When adding the same value to both sides of an equation, you are essentially canceling out the constant on the left-hand side of the equation. When subtracting the same value from both sides of an equation, you are essentially canceling out the constant on the right-hand side of the equation.

Order of Operations (PEMDAS)

  • Q: Why is the order of operations (PEMDAS) important?
    • A: The order of operations (PEMDAS) is important because it ensures that mathematical expressions are evaluated consistently and accurately.
  • Q: What happens if I don't follow the order of operations (PEMDAS)?
    • A: If you don't follow the order of operations (PEMDAS), you may get incorrect results or even change the meaning of the expression.

Tips and Tricks

  • Always follow the order of operations (PEMDAS) when simplifying expressions.
  • Combine like terms to simplify expressions.
  • Eliminate unnecessary parentheses to simplify expressions.
  • Isolate variables by getting rid of constants and other variables.
  • Check your work by plugging the solution back into the original equation.

Related Topics

  • Algebraic equations
  • Simplifying expressions
  • Isolating variables
  • Order of operations (PEMDAS)

Further Reading

  • For more information on algebraic equations, check out our article on "Solving Linear Equations".
  • For more information on simplifying expressions, check out our article on "Simplifying Algebraic Expressions".
  • For more information on isolating variables, check out our article on "Isolating Variables in Algebraic Equations".
  • For more information on the order of operations (PEMDAS), check out our article on "Understanding the Order of Operations (PEMDAS)".