Problem 108 - Beginning and Intermediate Algebra

Question

Twice the product of -1 and \(6,\) subtracted from -4

Step-by-Step Solution

Answer

8

Step 1: Identify the components

Recognize that the problem involves multiplication and subtraction. The components are -1, 6, and -4.

Step 2: Calculate the product

Multiply -1 and 6:\(-1 \times 6 = -6\)

Step 3: Double the product

Calculate twice the product obtained in Step 2:\(2 \times -6 = -12\)

Step 4: Subtract from -4

Subtract the result from -4 as follows:\(-4 - (-12)\)

Step 5: Simplify the expression

Simplify the subtraction:\(-4 + 12 = 8\)

Key Concepts

Multiplication

Multiplication is an arithmetic operation that combines groups of equal sizes. In this exercise, we are multiplying two numbers, -1 and 6.
When you multiply two numbers, like -1 and 6, follow these steps:

• Determine the sign of the result: The product of a negative number and a positive number is always negative.
• Multiply the absolute values of the numbers: \(-1 \times 6 = -6\).
• Combine the sign and the product: The result is \-6\.

Understanding the properties of multiplication helps solve more complex problems easily.

Subtraction

Subtraction is finding the difference between two numbers. In algebra, it's crucial to understand how to handle signs correctly.
In this exercise, we are subtracting twice the product of -1 and 6 from -4. Here are the steps to follow:

• Identify the numbers involved: We have -4 and -12 (which is twice the product of -1 and 6).
• Rewriting Subtraction as adding the opposite: \(\text{-4 - (-12) = -4 + 12}\) – because subtracting a negative number is the same as adding a positive number.
• Simplify the expression: Add -4 and 12, which results in 8.

Breaking down subtraction into these steps makes the process easier to understand.

Simplifying Expressions

Simplifying expressions means making them easier to work with by combining like terms and applying arithmetic operations.
In this exercise, we simplified \( \text{-4 - (-12)} \) by converting the subtraction of a negative number into an addition: \( \text{-4 + 12} \).
Tips for simplifying expressions:

• Combine like terms: Terms that have the same variable part or are constants can be added/subtracted.
• Apply arithmetic operations: Use basic operations like addition, subtraction, multiplication, and division.
• Use parentheses to group terms clearly: This avoids mistakes, especially with negative numbers.

Following these tips simplifies even the simplest expressions and helps solve algebra problems correctly.