Problem 113 - Algebra A Combined Function

Question

Write any expression, using 3 or more numbers, that simplifies to -11.

Step-by-Step Solution

Answer

-15 + 4 + 0 = -11.

Step 1: Write the Expression

Start by choosing a combination of numbers that, when added or subtracted, will give the result of -11. Let's use three numbers: -15, +4, and 0. These numbers will form the expression: \(-15 + 4 + 0\).

Step 2: Simplify the Expression

Now simplify the expression by performing the addition and subtraction from left to right. Start with \(-15 + 4\), which equals \(-11\). Then add \(0\) to \(-11\), which still results in \(-11\).

Step 3: Final Expression and Verification

The expression \(-15 + 4 + 0\) simplifies to \(-11\). To verify, start with \(-15\), add \(4\) to get \(-11\), and adding \(0\) changes nothing, leaving the final result as \(-11\).

Key Concepts

Simplification of Expressions

Simplification is a fundamental concept in algebra. It involves reducing an expression to its simplest form without changing its value. For instance, when you have an algebraic expression like \(-15 + 4 + 0\), you want to perform operations to make it as simple as possible.
The goal is to combine terms in a way that eliminates unnecessary components and highlights the most straightforward version, such as reaching a single number.
This not only makes expressions easier to work with

• Identify and group like terms.
• Perform operations, such as addition and subtraction, using the correct order.
• Ensure the expression is fully simplified by the end.

Simplification can involve several mathematical operations, but often focuses heavily on addition and subtraction of numbers, as it does in this case.

Integers

Integers are whole numbers that can be positive, negative, or zero. These numbers do not have decimals or fractions and can be essential in solving algebraic expressions.
In our example expression \(\-15 + 4 + 0\), all numbers involved are integers.

• -15 is a negative integer.
• 4 is a positive integer.
• 0 acts as the neutral element in addition and subtraction.

Working with integers is crucial because they allow you to perform calculations that define the structure and results of algebraic problems.
When using integers, it's important to remember:

• Negative integers reduce other values when added.
• Positive integers increase values when added.
• Zero does not affect the total when added or subtracted.

Addition and Subtraction

These are two basic operations in mathematics that are key to simplifying expressions. Addition involves combining values, while subtraction involves taking away.
To solve the expression \(-15 + 4 + 0\), we apply both of these operations.
Start by adding and subtracting from left to right, which is a standard method for handling operations without parentheses.

• Begin with the first two numbers: -15 and +4. Adding these gives -11.
• Next, add 0 to -11, which keeps it unchanged at -11.

Remember:

• Adding a positive number increases the sum, while adding a negative number decreases it.
• Subtraction can be seen as adding a negative number.
• The order of operations can affect the outcome if not done methodically.

Understanding and mastering these operations will allow you to simplify even more complex expressions accurately and efficiently.