Problem 45 - Algebra 1

Question

Evaluate the expression for the given value of x. $$-24+6+x ; x=8$$

Step-by-Step Solution

Answer

-10

Step 1: Substitution

Substitute the value of x in the given equation. So, the equation \( -24+6+x \) becomes \( -24+6+8 \)

Step 2: Perform the addition and subtraction

Perform the addition and subtraction from left to right. Calculate \( -24+6 \) first, which is \( -18 \). Then, add \( -18 + 8 \) to get \( -10 \)

Key Concepts

Substitution in Algebra

Substitution is the first step in the process of evaluating algebraic expressions. When you are given an expression and a specific value for a variable, substitution involves replacing the variable with the given number. Let's take the provided exercise as an example to illustrate this concept.

Starting with the expression \( -24+6+x \), we are told that \( x=8 \). To substitute the value of \( x \), we simply replace \( x \) with \( 8 \) in the expression. The original expression \( -24+6+x \) becomes \( -24+6+8 \). This transformed expression no longer contains the variable \( x \) and is ready for the next steps in the evaluation process – performing arithmetic operations.

Performing Arithmetic Operations

After substituting the variable with its value, performing arithmetic operations follows. In our example, we are now working with the expression \( -24+6+8 \), which involves two basic operations: addition and subtraction. When approaching arithmetic operations, we work from left to right, as we do in regular reading order.

We begin by adding \( -24 \) and \( 6 \) to get \( -18 \). Then, we move to the next step, adding \( 8 \) to our result of \( -18 \) to yield the final result of \( -10 \). This step-by-step approach ensures we maintain clarity and accuracy in our calculations. Arithmetic operations are the building blocks of more complex mathematical problem-solving, and mastering them is crucial for success in algebra and beyond.

Order of Operations in Algebra

The order of operations, known as PEMDAS or BODMAS, is crucial for correctly evaluating expressions in algebra. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS refers to Brackets, Orders (which are exponents such as squares and cube roots, etc.), Division, Multiplication, Addition, and Subtraction.

Let's reflect on how this applies to our problem \( -24+6+8 \). Since there are no parentheses, exponents, multiplication, or division, we directly proceed with addition and subtraction. Consistently applying the order of operations ensures that we reach the correct solution regardless of the complexity of the problem. Remembering to perform operations in this specific order avoids common mistakes and allows for accurate and unambiguous solutions in algebra.