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Chapter 1: Problem 105

Simplify. $$ -93+(-84)-(-93)-(-84) $$

Short Answer

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Step by step solution

01

Simplify the Negative Terms

Start by rewriting all the negative terms to make them easier to combine. Recall that subtracting a negative is equivalent to adding a positive: $$-93 + (-84) - (-93) - (-84)$$ becomes: $$-93 + (-84) + 93 + 84$$
02

Combine the Positive and Negative Pairs

Next, combine the terms with the same value but opposite signs. $$-93$$ and $$93$$ cancel each other out: $$-93 + 93 = 0$$ $$-84$$ and $$84$$ cancel each other out: $$-84 + 84 = 0$$
03

Sum Up All Remaining Values

Now, sum the results from the previous step:$$0 + 0 = 0$$

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Key Concepts

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

Negative Numbers
Negative numbers can sometimes be tricky, but they are just numbers to the left of zero on the number line. When you add negative numbers, you move to the left. When you subtract a negative number, it's like adding the positive version of that number. For example, subtracting \(- - 84\) is the same as adding \(+ 84\). This is what we call the 'double negative' concept. When you see double negatives, always remember to turn them into positive.
Combining Like Terms
When simplifying expressions, it is crucial to combine like terms. Like terms are numbers or variables that have the same value. Consider the terms \(-93\) and \(+93\). They are like terms because they have the same value but opposite signs.
Similarly, \(-84\) and \(+84\) are also like terms.
  • First, recognize the like terms in the expression.
  • Next, pair them together.
  • Then, combine them to simplify the expression.
In the given exercise, we have:
$$-93 + (-84) - (-93) - (-84)$$
This becomes:
$$-93 + (-84) + 93 + 84$$
Notice how \(-93\) and \(+93\) are paired, as well as \(-84\) and \(+84\).

This method makes the whole expression easier to simplify.
Algebraic Simplification
Algebraic simplification is the process of making an algebraic expression easier to understand. This involves combining like terms and dealing with negative numbers efficiently.
Let's look at the simplified terms we had:
$$-93 + (-84) + 93 + 84$$
We can see that: $$-93 + 93 = 0$$
and $$-84 + 84 = 0$$
Finally, we combine the results: $$0 + 0 = 0$$.
The entire expression simplifies to zero!
Here's a quick recap:
  • First, convert double-negative terms to positive.
  • Combine like terms (both positive and negative).
  • Simplify the terms step-by-step until you reach the simplest form.
By following these steps, you'll find algebra simpler and easier to handle.

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