Problem 84 - Algebra A Combined Function

Question

Evaluate each expression. \(-4(3-9)\)

Step-by-Step Solution

Answer

The result of the expression is 24.

Step 1: Evaluate the Expression Inside the Parentheses

First, solve the expression inside the parentheses: \(3 - 9\). This gives us \(-6\). So the expression simplifies to \(-4(-6)\).

Step 2: Multiply the Result by the Negative Number

Next, multiply the result from the parentheses by \(-4\). This means calculating \(-4 \times -6\), which results in \(24\) because the product of two negative numbers is positive.

Key Concepts

Evaluating Expressions

Evaluating expressions is a fundamental part of algebra that involves simplifying a series of operations to find a single value. At its core, it means replacing variables with numbers and following mathematical operations to reach a result. When you evaluate an expression, you must perform the operations in the correct order to arrive at the right answer.Consider the expression \[-4(3-9)\]. The first step is to look inside any parentheses, as these represent a collection of numbers or operations that should be evaluated as a single unit. In this exercise, the parentheses contain \[3-9\]. Replace this part with its evaluation result, \[-6\], to simplify the expression to \[-4(-6)\].Once you have simplified it as much as possible, you can proceed with other operations, like multiplication or addition, according to the rules of algebra. Thus, evaluating expressions requires careful attention to the structure of the equation and the operations within it.

Order of Operations

In algebra, it is crucial to perform calculations in the correct order. This sequence of operations is commonly referred to as the order of operations, and abiding by this order ensures that you obtain the correct result. The common acronym to remember this order is PEMDAS:

• Parentheses – solve anything in parentheses first
• Exponents – evaluate exponents next
• Multiplication and Division – from left to right
• Addition and Subtraction – from left to right

Let’s apply the order of operations to the expression \[-4(3-9)\]. The first step is to evaluate the parentheses: \[3-9 = -6\]. Once this is done, you’re left with \[-4(-6)\]. Since the expression now consists of multiplication only, you simply multiply the two numbers. Following the order of operations consistently helps avoid errors and leads to correct solutions.

Multiplying Negative Numbers

Understanding how to multiply negative numbers is an essential skill in algebra. Multiplying two negative numbers can be tricky at first because it may not seem intuitive that the product is positive.Here’s why: consider \[-4\] multiplied by \[-6\]. First, acknowledge that each negative number represents a direction away from zero on the number line. When you multiply these, you essentially reverse the direction twice. Thus, two negatives make a positive.So, \[-4(-6) = 24\]. This rule applies in any situation where you multiply two negative numbers:- A negative times a negative always results in a positiveThis mathematical rule is not only theoretically sound but also practically applicable in various real-world scenarios. It shows consistency across different cases and is integral to understanding more complex algebraic operations.