Evaluate The Expression ${ 2(x-4)\$} When { X = -3$}$.

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Introduction

In mathematics, evaluating an expression involves substituting a given value for a variable and simplifying the resulting expression. In this discussion, we will evaluate the expression ${2(x-4)\$} when {x = -3$}$. This involves substituting {x = -3$}$ into the expression and simplifying the result.

Understanding the Expression

The given expression is ${2(x-4)\$}. This expression involves a variable {x$}$ and a constant {-4$}$. The expression is enclosed in parentheses, indicating that the operation inside the parentheses should be performed first. The expression can be read as "2 times the quantity {x$}$ minus 4".

Substituting the Value of {x$}$

To evaluate the expression, we need to substitute {x = -3$}$ into the expression. This involves replacing {x$}$ with {-3$}$ in the expression.

Evaluating the Expression

Substituting {x = -3$}$ into the expression ${2(x-4)\$}, we get:

${2(-3-4)\$}

Simplifying the Expression

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

  1. Evaluate the expression inside the parentheses: {-3-4 = -7$}$
  2. Multiply 2 by the result: ${2 \times -7 = -14\$}

Conclusion

Therefore, the value of the expression ${2(x-4)\$} when {x = -3$}$ is {-14$}$.

Step-by-Step Solution

Here's a step-by-step solution to the problem:

  1. Substitute the value of {x$}$: Replace {x$}$ with {-3$}$ in the expression ${2(x-4)\$}.
  2. Evaluate the expression inside the parentheses: Simplify the expression inside the parentheses: {-3-4 = -7$}$
  3. Multiply 2 by the result: Multiply 2 by the result: ${2 \times -7 = -14\$}

Final Answer

The final answer is {-14$}$.

Related Problems

If you want to practice more problems like this, here are some related problems:

  • Evaluate the expression ${3(x+2)\$} when {x = 5$}$
  • Evaluate the expression ${4(x-1)\$} when {x = 2$}$
  • Evaluate the expression ${2(x+3)\$} when {x = -1$}$

Tips and Tricks

Here are some tips and tricks to help you evaluate expressions like this:

  • Always follow the order of operations (PEMDAS)
  • Substitute the value of the variable into the expression
  • Simplify the expression by following the order of operations
  • Check your work by plugging in a simple value for the variable

Conclusion

Evaluating an expression involves substituting a given value for a variable and simplifying the resulting expression. In this discussion, we evaluated the expression ${2(x-4)\$} when {x = -3$}$. We substituted the value of {x$}$ into the expression, simplified the result, and arrived at the final answer of {-14$}$.

Introduction

Evaluating expressions is a fundamental concept in mathematics. In our previous discussion, we evaluated the expression ${2(x-4)\$} when {x = -3$}$. In this Q&A article, we will address some common questions and provide additional examples to help you understand how to evaluate expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS is commonly used to remember the order of operations:

  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 evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, follow the order of operations:

  1. Evaluate any expressions inside parentheses.
  2. Evaluate any exponential expressions.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What if I have a variable with a negative exponent?

A: When you have a variable with a negative exponent, you can rewrite the expression using the rule {a^{-n} = \frac{1}{a^n}$}$. For example, {x^{-2} = \frac{1}{x^2}$}$.

Q: How do I evaluate an expression with a fraction?

A: To evaluate an expression with a fraction, follow the order of operations:

  1. Evaluate any expressions inside parentheses.
  2. Evaluate any exponential expressions.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What if I have a variable with a coefficient?

A: When you have a variable with a coefficient, you can multiply the coefficient by the variable. For example, ${3x = 3 \times x\$}.

Q: How do I evaluate an expression with a negative value?

A: To evaluate an expression with a negative value, follow the order of operations:

  1. Evaluate any expressions inside parentheses.
  2. Evaluate any exponential expressions.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What if I have a variable with a decimal value?

A: When you have a variable with a decimal value, you can multiply the decimal value by the variable. For example, ${2.5x = 2.5 \times x\$}.

Q: How do I evaluate an expression with a variable in the denominator?

A: To evaluate an expression with a variable in the denominator, follow the order of operations:

  1. Evaluate any expressions inside parentheses.
  2. Evaluate any exponential expressions.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What if I have a variable with a negative value in the denominator?

A: When you have a variable with a negative value in the denominator, you can rewrite the expression using the rule {\frac{1}{-a} = -\frac{1}{a}$}$. For example, {\frac{1}{-x} = -\frac{1}{x}$}$.

Q: How do I evaluate an expression with a variable in the numerator and denominator?

A: To evaluate an expression with a variable in the numerator and denominator, follow the order of operations:

  1. Evaluate any expressions inside parentheses.
  2. Evaluate any exponential expressions.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Conclusion

Evaluating expressions is a fundamental concept in mathematics. By following the order of operations and understanding how to evaluate expressions with variables, fractions, and negative values, you can become proficient in evaluating expressions. Remember to always follow the order of operations and simplify the expression by following the order of operations.