Problem 29 - Elementary and Intermediate Algebra

Question

Find \(-(-x)\) when \(x\) is each of the following. $$ 72 $$

Step-by-Step Solution

Answer

72

Step 1: Understand the expression

The expression \(-(-x)\) means taking the negative of the negative of \(x\).

Step 2: Apply the expression to the given value

Substitute \(x = 72\) into the expression. This yields: \(-(-72)\).

Step 3: Simplify the expression

A negative sign in front of another negative sign cancels out. Therefore, we have: \(-(-72) = 72\).

Key Concepts

Negative Numbers

Let's take a look at negative numbers. Negative numbers are less than zero, and they are often indicated by a minus sign (-) placed before the number. For instance, -5 is five units below zero on a number line. It's important to note that when you multiply or divide two negative numbers, the result is positive.

Here's a useful tip: If you have two negative signs in front of a number, they cancel each other out and turn positive. This is central to solving problems like \(-(-x)\). In this case, the double negative in front of \(72\) becomes a positive 72.

Keep practicing working with negative numbers, as they are foundational to understanding algebraic expressions.

Substitution

Substitution is a method used in algebra to replace variables with their corresponding values. In our problem, we are asked to find \(-(-x)\) when \(x = 72\). Substituting simply means replacing the variable \(x\) with its given value.

So, if \(x = 72\), we replace \(x\) in the expression \(-(-x)\) with 72. This makes our expression \(-(-72)\).

Substitution makes complex equations simpler and more understandable. It's a powerful tool in algebra!

Simplification

Simplification is the process of making an expression easier to understand and solve. With algebraic expressions, we often use simplification to combine like terms or perform arithmetic operations.

In the given problem, after substituting \(x = 72\) and obtaining \(-(-72)\), we need to simplify it. Simplification reveals that two negative signs cancel each other out. Therefore: \-(-72) = 72\.

Practice simplifying different algebraic expressions to become more comfortable solving more complex problems!