Problem 32 - Elementary and Intermediate Algebra

Question

Find \(-(-x)\) when \(x\) is each of the following. $$ -9.1 $$

Step-by-Step Solution

Answer

-9.1

Step 1: Understand the Double Negative

When dealing with the expression \(-(-x)\), recognize that the double negative will cancel each other out, effectively leaving just \(x\).

Step 2: Substitute the Given Value

Substitute the given value \(-9.1\) for \(x\) in the expression.

Step 3: Simplify the Expression

Simplify \(-(-(-9.1))\). Since the double negative cancels out, the expression simplifies to \(-9.1\).

Key Concepts

double negative

Understanding the concept of a double negative in mathematics is important for various algebraic operations. A double negative occurs when two negative signs are next to each other. The rule to remember is that two negatives will cancel out, resulting in a positive.
For example, if we encounter \(-(-x)\), the double negative effectively **removes** the negatives, leaving us with just \(x\). This holds true for numbers and variables alike, simplifying calculations and expressions.

simplification

Simplification in mathematics is all about reducing an expression to its simplest form. This means performing all possible operations to combine like terms and remove any unnecessary complexity.
In our example, the expression is \(-(-x)\). By recognizing the double negative, we can immediately simplify this to \(x\). Substituting \(-9.1\) for \(x\) leads us to \(-(-(-9.1))\). Since the double negative cancels out, the simplified expression is just \(-9.1\).
It's like untying a knot: once you've simplified, everything becomes much clearer and easier to understand.

substitution

Substitution is a crucial step in solving algebraic expressions as it allows you to replace a variable with a specific value. By doing this, abstract expressions become concrete numbers, simplifying computations.
For instance, in our problem, we start with \(-(-x)\). Once we understand that the double negatives cancel out, we substitute \(-9.1\) for \(x\). With this substitution, our expression becomes \(-(-(-9.1))\). Simplifying this gives us \(-9.1\).
Substituting values correctly can help solve equations more quickly and accurately, turning complex problems into straightforward solutions.