Problem 61 - Algebra 1: Concepts and Skills

Question

What does \(-x-7\) equal when \(x=-1 ?\) F. \(-8\) G. \(-6\) H. 6 J. 8

Step-by-Step Solution

Answer

The correct answer is G. -6

Step 1: Substitute

Replace \(x\) in the equation \(-x-7\) with the given value, \(-1\). This results in \(-(-1)-7\).

Step 2: Simplify

Simplify \(-(-1)-7\) by dealing with the double negative first, which results in \(1-7\).

Step 3: Find the Final Value

Subtract \(7\) from \(1\) to get the final value, \(-6\)

Key Concepts

Substitution Method

Understanding the substitution method is crucial when solving linear equations. It allows us to find the value of an expression by replacing variables with given numbers.

For instance, in the exercise, we are asked to determine the value of \( -x-7 \) when \( x=-1 \). The substitution method comes into play by taking the given value of \( x \) and substituting it into the equation. We replace \( x \) with \( -1 \) which transforms the equation to \( -(-1)-7 \). It's a straightforward process, but it requires careful attention to ensure that the replacement is done accurately.

Negative Numbers

Dealing with negative numbers can be tricky, but with careful application of rules, it can become simple. In our exercise, we confront the concept of a 'double negative'. A double negative occurs when two negative signs are next to each other, as in \( -(-1) \).

It's important to remember that two negatives make a positive; thus, \( -(-1) \) becomes \( 1 \). This rule is pivotal to solving equations accurately and is a fundamental block of arithmetic operations with negative numbers.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. These operations are the building blocks for all of mathematics.

In the context of our problem, we perform subtraction after dealing with the double negative. Once we've substituted and simplified \( -(-1)-7 \) to \( 1-7 \) using the rules for negative numbers, we then apply subtraction. Taking away \( 7 \) from \( 1 \) leads us to the final answer, \( -6 \). Understanding the correct order in which to perform arithmetic operations is essential for working through equations methodically and accurately.