Problem 31 - Elementary and Intermediate Algebra

Question

Find \(-(-x)\) when \(x\) is each of the following. $$ -\frac{2}{5} $$

Step-by-Step Solution

Answer

\( -(-(-\frac{2}{5})) = \frac{2}{5} \)

Step 1 - Understand the Problem

We need to find the value of \(-(-x)\) when \(x\) is \(-\frac{2}{5}\). This involves simplifying the expression by eliminating the double negative.

Step 2 - Substitute the Given Value

Given that \(x = -\frac{2}{5}\), substitute this value into the expression \(-(-x)\)\.

Step 3 - Simplify the Double Negative

The expression \(-(-x)\) becomes \(-(-(-\frac{2}{5}))\). Simplifying this, we notice that the two negatives cancel each other out: \-(-(-\frac{2}{5})) = -\frac{2}{5}\. Hence, \(-(-(-\frac{2}{5})) = \frac{2}{5}\).

Key Concepts

double negatives in algebra

Double negatives in algebra can be confusing, but understanding how they work is important. When you see a double negative, it means that the two negatives cancel each other out. For example, consider the expression \(-(-x)\). The first negative sign inside the parentheses changes the value of \x\ into its opposite. The second negative sign outside the parentheses then reverses this change, bringing us back to the original value of \x\. It's much like saying 'not not happy' which just means 'happy'.
Let’s see another example: if x is \-3\, then \-(-(-3)) = 3\.
Remember, every pair of negatives can be eliminated, which simplifies your computations.

substitution in algebra

Substitution in algebra helps to find the value of an expression by replacing variables with specific values. This method is used to simplify and solve problems effectively. In our exercise, we are asked to find \-(-x)\ when \ x\ is given as \-\(\frac{2}{5}\)\.

• First, identify the given value: \ x = -\(\frac{2}{5}\) \.
• Next, substitute \ x \ with \ -\(\frac{2}{5}\) \ in the expression: \-(-x)\ becomes \-(-(-\frac{2}{5}))\.

After substitution, we simplify the double negative, which helps to solve the problem.

fraction operations

Working with fractions in algebra requires careful attention to detail. When dealing with negative fractions, pay close attention to the signs. In the given exercise, \ x = -\(\frac{2}{5}\)
When we substitute this into the expression \ -(-(-\frac{2}{5}))\, we simplify by removing the double negative.

• First negative makes \-\frac{2}{5}\ a positive value \ \frac{2}{5}\.

By converting the value and eliminating double negatives, you simplify the algebraic fraction operations to get the final result.