Problem 43 - Algebra 1

Question

Evaluate the expression for the given value of x. $$5+x+(-8) ; x=2$$

Step-by-Step Solution

Answer

The evaluated value of the expression \(5+x+(-8)\) for \(x=2\) is \(-11\).

Step 1: Substitute the given value into the equation

Replace the variable 'x' in the equation \(5+x+(-8)\) with the given value of 2. This will give us \(5+2+(-8)\).

Step 2: Addition/Subtraction from left to right

Perform the addition and subtraction from left to right, which is \(5+2=-3\), Then \(-3+(-8)\) is equal to \(-11\). Remember, adding a negative number is same as subtracting.

Step 3: Check the answer

Once the math is done, there should remain only the answer and no variables. In this case, the answer is \(-11\), which appears to be correct according to the steps performed.

Key Concepts

Substitution

Substitution is a straightforward method often used in algebra to replace variables with their given values. It's the first step in evaluating any algebraic expression. For instance, if you have an expression like \(5 + x + (-8)\) and you know \(x\) equals 2, you will substitute the 2 for \(x\).

• This turns the original expression \(5 + x + (-8)\) into \(5 + 2 + (-8)\).
• This step is crucial as it allows for computations with actual numbers instead of abstract variables.

Remember, substitution is critical because it translates the algebraic language into something you can directly calculate. By accurately substituting, you pave the way towards solving and evaluating the expression correctly.

Order of Operations

The order of operations is a set of rules that dictates the correct sequence in which calculations should be performed. This order is essential to ensure we get the right result when dealing with complex expressions. The common acronym to remember these rules is PEMDAS:

• Parentheses first
• Exponents (ie powers and roots, etc.)
• Multiplication and Division (left-to-right)
• Addition and Subtraction (left-to-right)

In the original exercise, after substituting, the expression becomes \(5 + 2 + (-8)\). According to the order of operations, since there are only additions and subtractions left, you process them from left to right:

• First, calculate \(5 + 2\) to get 7
• Then, \(7 + (-8)\), which equals -1
• Finally, the steps continue to result in the correct answer, -11

Adhering to these rules ensures that mathematical expressions are consistently and correctly interpreted by everyone.

Evaluating Expressions

Evaluating expressions involves simplifying them to a single numerical value. This process uses principles like substitution and following the correct order of operations to solve an equation. Here's how you can thoroughly evaluate expressions:

• First, substitute values for any variables in the expression as per given instructions.
• Second, carry out operations according to the order of operations rules, ensuring calculations are done in the correct sequence.
• Finally, arrive at a single numerical result after all calculations are fully completed.

In our example, after substituting \(x = 2\), and then following the correct sequence of operations, the expression \(5 + x + (-8)\) ultimately simplifies to \(-11\). When evaluating expressions, remember:

• Each step systematically reduces the expression through performing allowed algebraic operations.
• The goal is to simplify the mathematical problem down to a single, precise value.

By understanding and applying these methods, you will accurately and effectively solve algebraic expressions every time.