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Chapter 10: Problem 64

Evaluate \(-(-x)\) when: $$ x=-7.1 $$

Short Answer

Expert verified
7.1

Step by step solution

01

Substitute the value of x

Replace the variable x with -7.1 in the given expression. The expression \(-(-x)\) becomes \(-(-(-7.1))\).
02

Simplify the double negative

A double negative in an expression cancels out, turning it into a positive. Therefore, \(-(-(-7.1))\) becomes \(7.1\).

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Key Concepts

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

Substituting Values
When evaluating expressions, one of the key steps is substituting values. This means replacing a variable with a specific number. Let's look at our example: we start with the expression \(-(-x)\).
Given that \(x=-7.1\), we substitute this value into the expression. So, \(-(-x)\) turns into \(-(-(-7.1))\).
This helps us convert an abstract mathematical expression into something more concrete and easier to work with. Understanding how to correctly substitute values is crucial for solving algebraic expressions.
Simplification
After substituting values, the next core concept is simplification. Simplification involves reducing the complexity of an expression without changing its value. This process often includes:
  • Combining like terms
  • Removing parentheses
  • Rewriting expressions in a simpler form
In our case with \(-(-(-7.1))\), we need to simplify the nested negatives. Simplifying helps in solving expressions faster and with fewer errors.
Double Negative
A double negative in mathematics cancels out and turns into a positive. This can be tricky, but it's a simple rule: two negatives make a positive.
In our example, \(-(-(-7.1))\) contains a double negative \(-(-(-7.1))\). By following the double negatives rule, \(-(-(-7.1))\) simplifies to \(7.1\). Remembering that a double negative equals a positive is essential for correctly evaluating expressions.
This rule can be applied whenever you encounter double negatives in various algebraic expressions.

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