Problem 8 Simplify. $$-5-27--\sqrt{3}$$... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 8: Problem 8

Simplify. $$-5-27--\sqrt{3}$$

Short Answer

Expert verified

The simplified expression is $-32 + \sqrt{3}$.

Step by step solution

Understand the Expression

The expression given is \[-5 - 27 - (-\sqrt{3}).\] The task is to simplify it by removing the minus signs and combining like terms.

Remove Double Negation

Since there is a double negative sign in \[ -(-\sqrt{3}) \] it will turn into a positive. Thus, we rewrite the expression as \[-5 - 27 + \sqrt{3}.\]

Combine Like Terms

Combine the constants $-5$ and $-27$: a) Start by adding the constants:\[-5 - 27 = -32.\]Now, rewrite the expression with the combined terms:\[-32 + \sqrt{3}.\]

Express the Simplified Form

The simplified expression is $-32 + \sqrt{3}$. It cannot be simplified further because $-32$ and $\sqrt{3}$ are unlike terms.

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Key Concepts

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

Understanding Minus Signs

Minus signs can often trip people up in algebra, especially when they appear in various spots within an expression. A minus sign before a number or a variable indicates its opposite:

Negative Numbers: A simple negative sign before a number makes it negative (e.g., $-5$ means we are looking at the opposite of $+5$.
Negative of a Negative: When you see a minus sign in front of a bracket, such as in $-(-3)$, it means the opposite of $-3$, which is $+3$.

In practice, pay close attention to minus signs, especially when dealing with the subtraction of negative numbers. Recognizing how they change the value is crucial in avoiding simple errors.

Double Negation: Making Negatives Positive

A double negation happens when you see two negative signs in a row. This can be a bit confusing, but there's a trick:

Double Negative Rule: When two negatives appear together, they cancel each other out, turning the negative into a positive.

For example, the expression $-(-\sqrt{3})$ changes to $+\sqrt{3}$. By understanding this simple rule, you can quickly simplify such parts of expressions.
Remembering that two negatives result in a positive will make simplification tasks more intuitive and less error-prone.

Combining Like Terms in Algebra

Combining like terms is an essential skill in algebra that helps simplify expressions. Here's what you need to know:

Like Terms: Terms that have the same variable raised to the same power, though they can have different coefficients. Constants (like numbers without variables) are also considered like terms among themselves.
Combining Process: Add or subtract their coefficients to simplify the expression. This process helps in reducing the expression to its simplest form.

In our original expression, $-5$ and $-27$ are both constants. You simply combine them by operation: $-5 - 27 = -32$.
After combining, we're left with $-32 + \sqrt{3}$, where no further combination is possible because $-32$ and $+\sqrt{3}$ are unlike terms.

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91影视

Simplify. $$-5-27--\sqrt{3}$$

Short Answer

Step by step solution

Understand the Expression

Remove Double Negation

Combine Like Terms

Express the Simplified Form

Key Concepts

Understanding Minus Signs

Double Negation: Making Negatives Positive

Combining Like Terms in Algebra

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