Problem 25 - Elementary Algebra

Question

\(-(-6)\)

Step-by-Step Solution

Answer

6

Step 1: Identify the problem

The problem requires evaluating the expression \(-(-6)\). This involves handling double negatives.

Step 2: Apply the double negative rule

According to mathematical rules, a double negative cancels out. Thus, \(-(-6)\) becomes simply 6.

Key Concepts

Double Negatives

When we talk about double negatives in algebra, we're referring to an expression that contains two negation signs. A negation in mathematics usually means changing the sign of a number. So, instead of positive, it becomes negative, and vice versa.

In the exercise \(-(-6)\), the first negation changes \(-6\) to positive 6 because the negative signs cancel each other out. Think of a negative sign as flipping the number to the opposite side on the number line. So, if you flip \(-6\) twice, you end up back at positive 6.

Key points to remember:

• Double negatives cancel each other out.
• Use them when simplifying expressions with two negations.
• In real-world terms, think of it as undoing an undo, which brings you back to the original state.

Evaluating Expressions

Evaluating an expression means finding its value by performing the operations given.

Take the expression \(-(-6)\). To evaluate this:

• First, identify and simplify any double negatives, as discussed. Apply the rule: a double negative equals a positive. So, \(-(-6)\) becomes 6.
• Confirm that no further operations are needed. No more additions or multiplications? You're done!

This step-by-step approach keeps things clear and reduces errors. Remember:

• Always simplify where possible.
• Look out for bracketed negatives.
• Follow the rules of arithmetic carefully.

Elementary Algebra

Elementary algebra is all about understanding and using basic rules to manipulate and simplify algebraic expressions.

Key topics include:

• Understanding operations: addition, subtraction, multiplication, and division.
• Knowing how to handle negative numbers and variables.
• Practicing the rules for dealing with square roots, exponents, and combining like terms.

For our example of \(-(-6)\):

This fits under handling negative numbers. Elementary algebra teaches us that two negatives make a positive. Thus, \(-(-6)\) results in 6.

Practice these principles with other numbers and expressions to build strong foundational skills in algebra.