Problem 12 - Intermediate Algebra

Question

Use a graphing calculator to check each exercise. $$ -13-4+9 $$

Step-by-Step Solution

Answer

The expression simplifies to -8.

Step 1: Simplify the Expression

The expression given is \(-13 - 4 + 9\). We will first perform the subtraction followed by the addition.

Step 2: Sub-Step 1.1: Perform Subtraction

Start by evaluating the subtraction part of the expression: \(-13 - 4 = -17\).

Step 3: Sub-Step 1.2: Perform Addition

Now, add the result from Sub-Step 1 to 9: \(-17 + 9\). This evaluates to \(-8\).

Step 2: Verify with Graphing Calculator

Enter the expression \(-13 - 4 + 9\) into the graphing calculator. Check if the result matches our manual calculation, which is \(-8\).

Key Concepts

Understanding Mathematical Expressions

Mathematical expressions are combinations of numbers and mathematical operation symbols like addition (+) and subtraction (-). They are fundamental in solving math problems. The problem here reads \(-13 - 4 + 9\). This is an example of an arithmetic expression. It's important to recognize each part: the numbers and the operations you need to perform.

• -13, -4, and 9 are constants.
• The operations here are subtraction and addition.

Understanding how to interpret and tackle these expressions is the first step in any math problem. Before simplifying, familiarize yourself with the components and operations involved.

Simplification of Expressions

Simplification refers to reducing a mathematical expression to its simplest form. This often involves combining like terms and applying mathematical operations. For the expression \(-13-4+9\), here’s how we simplify:

• Identify similar operations: both subtraction and addition need to occur.
• Follow the order of operations, which prioritizes subtraction first in this sequence.

Simplification makes calculations more straightforward and helps us in understanding the problem at a glance. Ensure each step is checked for accuracy, especially when negative numbers are involved, as they can change the operation’s outcome.

Mastering Addition

Addition is one of the basic arithmetic operations. It involves finding the total or sum by combining numbers. In our expression, after simplifying to \(-17 + 9\), addition can occur. During addition:

• Determine the overall sign by comparing absolute values.
• Combine the numbers: since the larger absolute value here is -17, the result will retain the negative sign.
• Calculate the sum: \(-17 + 9 = -8\).

Addition, particularly involving negative numbers, requires careful handling to ensure accurate results.

Subtraction Details

Subtraction is another key arithmetic operation, often resulting in a decrease or difference between two numbers. Begin by understanding the need for subtraction in the expression \(-13 - 4\). Follow these steps to perform subtraction:

• Remember that subtracting a number is the same as adding its opposite.
• For \(-13 - 4\), think of it as \(-13 + (-4)\).
• Combine these, effectively adding negatives, to get \(-17\).

Understanding this operation is especially important when dealing with negative values, as this often throws students off. Consistent practice of subtraction will build better mathematical intuition.