Problem 40 - Elementary Algebra

Question

Translate each sentence to a mathematical statement and then simplify. Subtract 6 from the difference of -1 and 7 .

Step-by-Step Solution

Answer

The mathematical statement becomes \(-1 - 7 - 6 = -14\).

Step 1: Identify the Components

First, we need to identify the components of the sentence. The sentence says "Subtract 6 from the difference of -1 and 7." Here, we find two key operations: the difference of -1 and 7, and then subtracting 6 from it.

Step 2: Write the Mathematical Expression

The difference between -1 and 7 is written mathematically as \[-1 - 7\].Then, we subtract 6 from this difference, which gives us the expression\[(-1 - 7) - 6\].

Step 3: Simplify the Expression

Now, let's simplify the expression. Start with the innermost operation:\(-1 - 7 = -8\).So, replace this in the expression to get:\[-8 - 6\].Further simplify by evaluating:\(-8 - 6 = -14\).

Key Concepts

Understanding Mathematical Statements

A mathematical statement is a way to represent a problem using numbers and symbols. It's like translating words into numbers, so mathematicians can understand and solve them easily. For example, when you have a sentence like "subtract 6 from the difference of -1 and 7," you need to find the operations involved.

Understanding these operations helps in forming the correct mathematical expression. In this exercise, "the difference of -1 and 7" becomes \(-1 - 7\), and then we subtract 6, creating the expression \((-1 - 7) - 6\). This translation into symbols makes it easier to perform calculations.

Expression Simplification Made Easy

Simplifying an expression means breaking it down into a simpler form. This makes it easier to understand and solve. In this exercise, we start with the expression \((-1 - 7) - 6\).

Simplification follows these steps:

• Calculate the innermost part first: \(-1 - 7 = -8\).
• Then solve the remaining part: \(-8 - 6 = -14\).

By doing this, you reduce the expression to its simplest form of \(-14\). Simplification helps you find the answer quickly and accurately.

Problem-Solving Steps Explained

Problem-solving involves a structured approach to tackle mathematical problems. Here’s how it works:

• Identify the components: Understand what the problem is asking. In this case, we needed to subtract and find differences.
• Write the expression: Translate words into mathematical notation (e.g., \((-1 - 7) - 6\)).
• Simplify: Perform calculations step-by-step, starting from the inside out.

By following these steps, you ensure nothing is missed, and you reach the correct answer efficiently. This structure is key in solving any algebraic problem with confidence.