Problem 43 - Algebra 1: Concepts and Skills

Question

EVALUATING EXPRESSIONS Evaluate the expression for the given value of the variable. \(-x-y\) when \(x=-2\) and \(y=-1\)

Step-by-Step Solution

Answer

The evaluated expression is 3.

Step 1: Identify the Expression and Variable Values

The expression given is \(-x - y\). The values provided for the variables are \(x = -2\) and \(y = -1\).

Step 2: Substitute the Variable Values

Next, substitute the values of the variables into the expression. This will give us: \(-(-2) - (-1)\).

Step 3: Simplify the Expression

After substituting, the expression simplifies to \(2 + 1\).

Step 4: Evaluate the Expression

The final step is to calculate the expression \(2 + 1\), which equals to 3.

Key Concepts

Variable Substitution

Variable substitution is a fundamental concept in algebra that allows us to replace variables in expressions or equations with specific values. This process enables us to evaluate expressions to yield actual numbers.

In the context of our exercise, you start by knowing what values your variables represent. Here, the expression given is \(-x - y\), where \(x = -2\) and \(y = -1\).

The substitution involves taking these supplied values and replacing their respective variables in the expression. For example:

• Replace \(x\) with \(-2\).
• Replace \(y\) with \(-1\).

By performing these substitutions, the expression \(-x - y\) turns into \(-(-2) - (-1)\). This sets the stage for evaluating and simplifying the expression further.

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It is like a sentence in math language that needs to be decoded using rules of algebra.

The expression \(-x - y\) is an algebraic expression composed of:

• Variable terms: \(x\) and \(y\).
• Coefficients: -1 as the implicit coefficients for both \(x\) and \(y\).
• Operations: Subtraction (\(-\)).

The primary goal of working with algebraic expressions is to perform operations like substitution, simplification, and eventually solving if it's an equation. In our case, we substitute the values of known variables into the expression, turning it into a numerical operation that can be evaluated.

Simplifying Expressions

Simplifying expressions involves reducing an algebraic expression to its most basic form. This often includes combining like terms, eliminating parentheses, or reducing arithmetic operations.

Once variable substitution is done, the expression \(-(-2) - (-1)\) allows us to perform simplification:

• Negating a negative converts it to a positive, so \(-(-2)\) becomes \(2\).
• Similarly, \(-(-1)\) becomes \(1\).

Simplification helps in making the expression much clearer and concise. After these operations, the simplified form is \(2 + 1\). Finally, evaluating this gives a result of \(3\).
The concept of simplifying is valuable as it allows anyone working with algebra to easily manage complex expressions and arrive at straightforward solutions.