Problem 41 - Algebra A Combined Function

Question

Translate each phrase to an expression and simplify. Decrease -8 by 15 .

Step-by-Step Solution

Answer

The expression for "Decrease -8 by 15" simplifies to -23.

Step 1: Identify the Numbers and Operations

First, we identify the numbers involved in the problem which are -8 and 15. The operation mentioned is 'decrease', which indicates subtraction.

Step 2: Set Up the Expression

Based on the word 'decrease', we need to subtract 15 from -8. This gives us the expression: \[-8 - 15\]

Step 3: Solve the Expression

To solve the expression, we perform the subtraction: -8 - 15 = -23.

Step 4: Simplify the Expression

The expression \(-8 - 15\) simplifies directly to \(-23\) as it is already expressed in its simplest form.

Key Concepts

Subtraction in Algebra

In algebra, subtraction is a fundamental operation used to find the difference between numbers. When a problem mentions that one value should "decrease" by another, it tells us to subtract the latter from the former. This concept is similar to subtraction in arithmetic, but in algebra, we might work with both numbers and variables.

To subtract two numbers, you write out the expression by positioning the numbers as stated in the problem. For example, if we need to find what happens when we decrease \(-8\) by \(15\), we set up the expression \(-8 - 15\). This shows that \(15\) is being subtracted from \(-8\).

When solving subtraction problems in algebra, it is essential to carefully interpret the words like "decrease," "less than," or "minus," as they each imply a subtraction operation.

Negative Numbers

Working with negative numbers can be challenging at first, but understanding them is crucial in algebra. Negative numbers are numbers with a minus sign (\(-\)) in front, indicating a value less than zero. They are used to represent debts, losses, or any value that's beneath the baseline.

In terms of subtraction, dealing with negative numbers means paying close attention to the signs. For instance, subtracting \(15\) from \(-8\) involves moving more to the negative side on the number line. Visualize this: if you're at \(-8\) and you subtract \(15\), you are essentially moving 15 full spaces to the left, landing at \(-23\).

Remember:

• When subtracting a positive number from a negative, you continue moving left on the number line.
• The larger the positive number you subtract, the more negative the result becomes.

Understanding the positioning of negative numbers in subtraction is vital for simplifying and solving algebraic expressions correctly.

Simplifying Expressions

Simplifying algebraic expressions involves breaking down expressions into their simplest form, ensuring there are no further calculations or reductions needed.

In our exercise, the expression was \(-8 - 15\). This was simplified directly to \(-23\). In practice, simplifying means you've completed all the operations: no other additions, subtractions, multiplications, or divisions are possible.

When simplifying expressions, always:

• Perform any obvious arithmetic operations first, such as addition or subtraction.
• Check if there are like terms that can be combined.
• Ensure variables, if any, are aligned correctly with coefficient values.

For expressions with only numbers, like \(-8 - 15\), simplifying often means just doing the straightforward math to achieve the cleanest and most direct result possible, as seen with the outcome \(-23\).