Select The Correct Answer To The Following Algebraic Expression:${ F \div -7 - 7 = -2 }$What Is The Value Of { F $}$?A. -35 B. 14 C. 5 D. -49 E. -12

Understanding the Problem

In this article, we will be solving an algebraic expression to find the value of the variable $f$. The given expression is:

$$f \div -7 - 7 = -2$$

Our goal is to isolate the variable $f$ and find its value.

Breaking Down the Expression

To solve this expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: None
2. Exponents: None
3. Multiplication and Division: Divide $f$ by $-7$
4. Addition and Subtraction: Subtract $7$ from the result

Step 1: Divide $f$ by $-7$

The first step is to divide $f$ by $-7$. This can be represented as:

$$\frac{f}{-7}$$

Step 2: Subtract $7$ from the Result

Next, we subtract $7$ from the result of the division:

$$\frac{f}{-7} - 7$$

Step 3: Set the Expression Equal to $-2$

We are given that the expression is equal to $-2$, so we can set up the equation:

$$\frac{f}{-7} - 7 = -2$$

Step 4: Add $7$ to Both Sides

To isolate the term with $f$, we add $7$ to both sides of the equation:

$$\frac{f}{-7} = -2 + 7$$

Step 5: Simplify the Right Side

Simplifying the right side of the equation, we get:

$$\frac{f}{-7} = 5$$

Step 6: Multiply Both Sides by $-7$

To solve for $f$, we multiply both sides of the equation by $-7$:

$$f = -7 \times 5$$

Step 7: Simplify the Right Side

Simplifying the right side of the equation, we get:

$$f = -35$$

Conclusion

Therefore, the value of $f$ is $-35$.

Answer

The correct answer is:

A. -35

Why is this the Correct Answer?

This is the correct answer because we followed the order of operations and isolated the variable $f$ by dividing both sides of the equation by $-7$ and then multiplying both sides by $-7$. This resulted in the value of $f$ being $-35$.

Tips and Tricks

• When solving algebraic expressions, always follow the order of operations (PEMDAS).
• Use parentheses to group terms and make the expression easier to read.
• When dividing or multiplying both sides of an equation by a variable, make sure to multiply or divide both sides by the same value.
• When adding or subtracting both sides of an equation by a constant, make sure to add or subtract the same value from both sides.

Common Mistakes

• Failing to follow the order of operations (PEMDAS).
• Not using parentheses to group terms.
• Not multiplying or dividing both sides of an equation by the same value.
• Not adding or subtracting the same value from both sides of an equation.

Real-World Applications

Algebraic expressions are used in a variety of real-world applications, including:

• Physics: Algebraic expressions are used to describe the motion of objects and the forces acting upon them.
• Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Conclusion

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

Q: What are the basic components of an algebraic expression?

A: The basic components of an algebraic expression are:

• Variables: Letters or symbols that represent unknown values.
• Constants: Numbers that do not change value.
• Mathematical operations: Addition, subtraction, multiplication, and division.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow the order of operations (PEMDAS):

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 solve an algebraic equation?

A: To solve an algebraic equation, follow these steps:

1. Isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
2. Use inverse operations to isolate the variable.
3. Check your solution by plugging it back into the original equation.

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

A: An algebraic expression is a mathematical expression that contains variables and constants, but does not contain an equal sign (=). An algebraic equation is a mathematical statement that contains an equal sign (=) and is used to solve for a variable.

Q: How do I evaluate an algebraic expression with exponents?

A: To evaluate an algebraic expression with exponents, follow these steps:

1. Evaluate any exponential expressions first.
2. Evaluate any multiplication and division operations from left to right.
3. Finally, 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 us which operations to perform first when evaluating an algebraic 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 use inverse operations to solve an algebraic equation?

A: To use inverse operations to solve an algebraic equation, follow these steps:

1. Identify the operation that is being performed on the variable.
2. Use the inverse operation to isolate the variable.
3. Check your solution by plugging it back into the original equation.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

• Linear expressions: Expressions that contain a single variable and a constant, such as 2x + 3.
• Quadratic expressions: Expressions that contain a squared variable, such as x^2 + 4x + 4.
• Polynomial expressions: Expressions that contain multiple variables and constants, such as 2x^2 + 3x - 4.

Q: How do I graph an algebraic expression?

A: To graph an algebraic expression, follow these steps:

1. Identify the type of graph that is being represented by the expression.
2. Use a graphing calculator or software to graph the expression.
3. Analyze the graph to identify any key features, such as x-intercepts and y-intercepts.

Q: What are some real-world applications of algebraic expressions?

A: Algebraic expressions have many real-world applications, including:

• Physics: Algebraic expressions are used to describe the motion of objects and the forces acting upon them.
• Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, algebraic expressions are a fundamental concept in mathematics that have many real-world applications. By understanding how to simplify, solve, and graph algebraic expressions, we can better analyze and solve problems in a variety of fields.