Problem 85 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. (Lesson 2.5) $$-3(x) \text { when } x=9$$

Step-by-Step Solution

Answer

The evaluated expression is \(-27\).

Step 1: Analyze the Expression

Given the algebraic expression \(-3(x)\), it's understood that this expression means \(-3\) multiplied by whatever value \(x\) holds.

Step 2: Substitute Value into Variable

Now, the given value for \(x\) is 9. Substitute 9 into the expression in place of \(x\) which gives \(-3(9)\).

Step 3: Calculate the Expression

The expression, \(-3(9)\), simplifies to \(-27\) because \(-3\) multiplied by 9 equals \(-27\)

Key Concepts

Substitution

Substitution is a key concept in algebra that involves replacing a variable in an expression with a given number. Here, our variable is \(x\), and the task is to substitute it with the value given. Substitution helps us simplify algebraic expressions and solve equations.

In the provided exercise, we need to substitute \(x=9\) into the algebraic expression \(-3(x)\). By doing this, you replace \(x\) with 9 in the expression, transforming it into \(-3(9)\).

• Identify the variable: Look at the variable in the given expression. In this case, it's \(x\).
• Use the given value: Replace \(x\) with the provided value, which is 9.

Understanding substitution is crucial for solving expressions and tackling more complex algebraic problems.

Remember: Substitution transforms expressions by assigning specific numerical values to variables.

Multiplication

Multiplication in algebra involves applying the basic rules of multiplying numbers to variables and coefficients. It helps simplify expressions and calculate the value of an expression after substitution.

In the exercise, after substituting \(x = 9\), you face the task of multiplication with \(-3(9)\). The process involves multiplying the constant part, \(-3\), by the substituted number, 9, to find the product. Here’s how it breaks down:

• Multiply the coefficient: Multiplier \(-3\) by 9, which includes sign consideration.
• Compute the product: The result of this multiplication is \(-27\).

Multiplication with negative numbers requires attention to signs. Remember, a negative times a positive results in a negative product, which is why \(-3(9) = -27\).

Proficiency in multiplication helps in evaluating expressions effectively.

Variables in Algebra

Variables are symbols, typically letters, representing numbers or values in algebraic expressions and equations. In algebra, they are placeholders for unknown or variable quantities.

For this exercise, \(x\) serves as a variable to be replaced by a specified number. Understanding the role of variables aids in structuring and solving expressions or equations. Important points to remember about variables include:

• Variables do not have fixed values; they can represent any number.
• They help form the backbone of algebraic expressions and equations.

When evaluating expressions, identifying and understanding variables allows you to see how changing their values affects the outcome.

Grasping how variables function is essential for algebraic manipulation and problem-solving.