Problem 93 - Elementary Algebra

Question

For exercises 15-100, evaluate. $$ (-6)(-5)-(-4) $$

Step-by-Step Solution

Answer

34

Step 1: Understand the Problem

The problem asks to evaluate the expression \( -6 \times (-5) - (-4) \). This involves multiplication and subtraction of negative numbers.

Step 2: Multiply the First Two Numbers

First, multiply \(-6\) and \(-5\). \(-6 \times -5 = 30\) because the product of two negative numbers is positive.

Step 3: Substitute the Result Back

Replace the multiplication part with the result from Step 2: \( 30 - (-4) \).

Step 4: Simplify the Expression

Next, subtract \(-4\) from 30. Subtracting a negative number is the same as adding the absolute value: \( 30 - (-4) = 30 + 4 \).

Step 5: Perform the Addition

Add 30 and 4: \( 30 + 4 = 34 \).

Step 6: State the Final Answer

After performing the addition, the final result is 34.

Key Concepts

Multiplying Negative Numbers

Negative numbers can sometimes be tricky. One important rule to remember is that when you multiply two negative numbers, the result is always positive.

For example, in the given exercise, we have \(-6 \times -5\). Since both numbers are negative, their product is positive.

This can be written as:
\(-6 \times -5 = 30\).
Understanding this rule helps to simplify a lot of algebraic expressions that involve multiplication.

Subtracting Negative Numbers

Subtracting negative numbers might seem confusing at first, but there's a simple trick. Subtracting a negative number is the same as adding its positive counterpart.

In the exercise, we encounter \(30 - (-4)\). This can be rewritten as \(30 + 4\).
Subtracting \(-4\) is like saying, 'let's add \4\'. So, \(30 - (-4)\) becomes \(30 + 4\), which equals \34\.

Simplifying Algebraic Expressions

Simplifying algebraic expressions means performing all possible operations to combine like terms.

For the given exercise, we combined the results of multiplying and subtracting negative numbers step by step.
We started with \(-6 \times -5 - (-4)\).
First, we handled the multiplication: \(-6 \times -5 = 30\).
Next, we worked on the subtraction: \(30 - (-4)\).
Simplifying that subtraction, we got: \(30 + 4 = 34\). Each step simplified the expression until we reached the final answer.

Absolute Value Addition

Absolute value represents the distance of a number from zero. For negative numbers, it's their positive counterpart.

When dealing with expressions like \(30 - (-4)\), we utilized the absolute value of \-4\.

Specifically, \-(-4)\ becomes \+4\.
This turns the expression into an easier addition problem: \(30 + 4\). Converting the subtraction of a negative number into an addition using absolute values makes algebra problems more straightforward.