Problem 46 - Algebra 1

Question

Evaluate the expression for the given value of x. $$-6+x+4 ; x=-3$$

Step-by-Step Solution

Answer

-5

Step 1: Substitute the given value.

Replace \(x\) with \(-3\) in \(-6+x+4\). That results to \(-6+(-3)+4\).

Step 2: Simplify the expression.

Perform the addition and subtraction from left to right. This first results in \(-9+4\), then simplifies further to \(-5\).

Key Concepts

Evaluate Expressions

Evaluating expressions is all about finding the value of an expression when specific numbers are substituted for the variables. It's like cracking a code by following a precise path. In our exercise, we're given the expression \(-6 + x + 4\) and need to find its value when \(x\) is \(-3\). The goal is to replace \(x\) with \(-3\) and then compute the result. This process helps in understanding how changes in variable values affect the overall expression.

• Identify the expression components.
• Substitute the given number for the variable.
• Calculate the final value.

Substitution

Substitution is like plugging in numbers where the variables are. It helps in turning an algebraic expression into something that can be easily solved. In our example, \(-6 + x + 4\), we substitute \(x\) with \(-3\). This means our expression becomes \(-6 + (-3) + 4\).

• Substitute accurately to avoid errors.
• Watch the signs, especially with negative numbers.
• This step simplifies the process by converting variables into known quantities.

Simplification

Simplification means making the expression as easy as possible by carrying out basic arithmetic operations in the correct order. After substitution, we have \(-6 + (-3) + 4\). We proceed by combining these numbers step by step.

• Start from left to right: \(-6 + (-3)\) becomes \(-9\).
• Next, add 4 to \(-9\) to find the final value.
• Ensure each step follows proper arithmetic rules.

Simplification allows us to see the expression in its simplest form, giving us an answer that's easy to understand.

Arithmetic Operations

Arithmetic operations are the basic actions of addition, subtraction, multiplication, and division used to simplify expressions. When simplifying \(-6 + (-3) + 4\), understanding arithmetic rules is crucial.

• Add numbers carefully: \(-6 + (-3)\) is the same as \(-6 - 3\), resulting in \(-9\).
• Continue by adding \(-9\) to 4, yielding \(-5\).
• Mastering these operations ensures accurate results every time.

These foundational skills not only help in evaluating expressions but are essential for more advanced algebra.