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Chapter 3: Problem 130

In the following exercises, model each expression and simplify. $$-6-(-4)$$

Short Answer

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Step by step solution

01

Identify the Expression

The given expression is $$-6-(-4)$$
02

Simplify the Double Negative

When subtracting a negative number, it is equivalent to adding its positive counterpart. Therefore, we can rewrite $$-6-(-4)$$ as $$-6 + 4$$
03

Perform the Addition

Add the numbers as indicated in the simplified expression: $$-6 + 4$$. This can be thought of in terms of direction on the number line. Starting from $$-6$$, move 4 steps to the right. The result is $$-2$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

double negative
In mathematics, dealing with double negatives can sometimes be tricky. A double negative appears when you have two negative signs together, usually in subtraction problems. It's important to know that \(-(-x)\) is the same as \(x\).

  • For instance, in the expression \(-6 - (-4)\), the \(-(-4)\) becomes \(+4\).
  • Thus, \(-6 - (-4)\) simplifies to \(-6 + 4\).

So, always remember, subtracting a negative is like adding a positive.
addition of integers
Adding integers involves combining positive and negative numbers. When you add a positive number to a negative number, you're essentially moving along the number line.
  • In the example \(-6 + 4\), you start at \(-6\) on the number line.
  • Moving 4 steps to the right (adding 4) lands you on \(-2\).
The sum of \(-6\) and \(+4\) is therefore \(-2\)

This method works for any integer addition, making it easier to visualize.
number line
A number line is a useful tool for visualizing operations with integers. It is simply a line with numbers placed at intervals, allowing you to move left for negative adjustments and right for positive ones.

  • To solve \(-6 + 4\), start at \(-6\) on the number line.
  • Move 4 units to the right to reach \(-2\).

Number lines help in understanding the addition and subtraction of integers, making abstract concepts more concrete.

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