Problem 1 - Elementary Algebra

Question

Evaluate for the given set of \(x\) -values. $$ 5 x ;\\{-1,0,1\\} $$

Step-by-Step Solution

Answer

-5, 0, 5

Step 1: Understand the Expression

The expression given is a simple linear function, which is \(5x\). Our task is to evaluate this expression for each \(x\)-value in the given set \{-1, 0, 1\}.

Step 2: Evaluate for \(x = -1\)

Substitute \(-1\) for \(x\) in the expression \(5x\):\[5(-1) = -5\]Thus, when \(x = -1\), the expression evaluates to \(-5\).

Step 3: Evaluate for \(x = 0\)

Substitute \(0\) for \(x\) in the expression \(5x\):\[5(0) = 0\]Thus, when \(x = 0\), the expression evaluates to \(0\).

Step 4: Evaluate for \(x = 1\)

Substitute \(1\) for \(x\) in the expression \(5x\):\[5(1) = 5\]Thus, when \(x = 1\), the expression evaluates to \(5\).

Key Concepts

Evaluating Expressions

Evaluating expressions is a fundamental skill in algebra that requires substituting specific values for variables and then simplifying the expression to find the result. When we talk about evaluating an expression like \(5x\), the aim is to determine what this expression equals for given values of \(x\). Consider the function \(5x\), where we want to find the value of this expression for different values of \(x\):

• For \(x = -1\), substitute and calculate \(5 \times -1 = -5\).
• For \(x = 0\), substitute and calculate \(5 \times 0 = 0\).
• For \(x = 1\), substitute and calculate \(5 \times 1 = 5\).

Breaking down each step helps avoid errors and ensures that we understand how changing the value of \(x\) affects the entire expression. Expressions can vary in complexity, but the principle of substituting and simplifying remains consistent across problems.

Substitution Method

The substitution method is a handy technique used in algebra to evaluate expressions or solve equations. It involves replacing a variable with a specific value to see what the expression or equation becomes. This is particularly useful for checking solutions or simplifying expressions where a variable might initially seem overwhelming.In our example, we have the expression \(5x\), and the task is to apply the substitution method using different values of \(x\) from a given set \{-1, 0, 1\}. Here's a simple breakdown:

• Determining the values to substitute by identifying them from the set provided.
• Substituting these values one by one for \(x\) in the expression \(5x\).

Applying the substitution method step by step allows you to specifically evaluate and understand the effect each substitution has on the overall expression.

Algebraic Expressions

Algebraic expressions like \(5x\) form the basis of algebra. They consist of variables, coefficients, and operations. In our example, \(5x\) includes:

• A variable \(x\), which represents unknown or varying quantities.
• A coefficient \(5\), which multiplies the variable \(x\).

Algebraic expressions can be simple, like our example, or more complex, involving multiple variables and operations. Understanding these components helps in manipulating and simplifying expressions effectively.The process of evaluating algebraic expressions involves understanding the structure of the expression and how it changes with different variable values. This skill is crucial for solving equations and understanding functions as you progress in algebra.