Problem 51 - Algebra A Combined Function

Question

Simplify each expression. \(2-3(8-6)\)

Step-by-Step Solution

Answer

The simplified expression is \(-4\).

Step 1: Identify the Expression to Simplify

The expression given is \(2-3(8-6)\). Our goal is to simplify this expression by resolving what's inside the parentheses first.

Step 2: Simplify Inside the Parentheses

Look inside the parentheses: \(8-6\). Perform the operation inside the parentheses: \(8-6 = 2\). Substitute back into the expression to get \(2-3(2)\).

Step 3: Perform Multiplication

Notice the expression is now \(2 - 3(2)\). Perform the multiplication: \(3 \times 2 = 6\). Substitute back into the expression to get \(2 - 6\).

Step 4: Finish with Addition/Subtraction

Now we simplify the expression \(2 - 6\). Perform the subtraction: \(2 - 6 = -4\). Thus, the simplified expression is \(-4\).

Key Concepts

Simplifying Expressions

Simplifying expressions is all about making a complex equation simpler to work with. Think of it like cleaning up a messy room. You want everything organized and easier to find. In math, simplifying involves reducing an expression to its most straightforward form. Here’s how to approach simplifying every time:

• Look for like terms: Numbers and variables that can be combined.
• Perform operations like addition, subtraction, multiplication, or division where possible.

By following these steps, you make your equations tidier. This helps when solving further problems or when needing a final simplified result. To effectively simplify, familiarity with mathematical basics, such as operations and order of operations, is essential.

Order of Operations

The order of operations is a set of rules that mathematicians agree on to avoid confusion when solving expressions. It's often remembered by the acronym PEMDAS, which stands for:

• Parentheses
• Exponents
• Multiplication and Division
• Addition and Subtraction

Each step must be followed in this specific order. For example, in the expression from the exercise, we first work on any arithmetic inside the parentheses. Next, look out for multiplication or division operations, which are handled from left to right. Lastly, tackle addition or subtraction, also from left to right. This ordered approach ensures everyone gets the same answer, avoiding calculation mix-ups.

Parentheses in Equations

Parentheses are powerful tools in mathematics. They signal which part of an expression you should calculate first, according to the order of operations. When you encounter parentheses, always perform calculations within them before anything else.

• Identify the operation inside the parentheses.
• Solve it and then replace the original part of the expression with the result.

In our exercise, the parentheses capture the operation \(8 - 6\), which simplifies to \(2\). This step is crucial as it can change the outcome of the overall expression dramatically. Parentheses help to manage complex expressions, ensuring the correct sequence of calculations and preventing errors.