Problem 4 - Intermediate Algebra

Question

Use a graphing calculator to check each exercise. $$ -5+(-9) $$

Step-by-Step Solution

Answer

The result of \(-5 + (-9)\) is \(-14\).

Step 1: Understand the Problem

We are asked to evaluate the expression \(-5 + (-9)\). This involves adding two negative numbers together.

Step 2: Arrange the Operation

In the expression \(-5 + (-9)\), first note that adding a negative number is equivalent to subtraction. So, we have \(-5 - 9\).

Step 3: Solve the Expression

Calculate \(-5 -9\): When combining these two negative values, think of it as moving further in the negative direction on a number line. The two numbers add as \(-5 + (-9) = -14\).

Step 4: Check with Graphing Calculator

Input the expression into a graphing calculator as \(-5 + (-9)\) or \(-5 - 9\) and verify the result. The calculator should confirm that the result is \(-14\).

Key Concepts

Graphing Calculator

A graphing calculator is a powerful tool that can help simplify and verify mathematical calculations, including when working with negative numbers. It is especially useful in visualizing complex problems and checking the accuracy of manual computations. To utilize a graphing calculator for expressions like -5 + (-9), follow these steps:

• Turn on the graphing calculator and access the main screen where calculations are entered.
• Type in the expression exactly as shown: \(-5 + (-9)\) or you can simplify it as \(-5 - 9\).
• Press "Enter" to compute the result.
• Observe the result displayed by the calculator, which should be \(-14\).

Graphing calculators provide precision and can graph functions, handle algebraic equations, and even contribute to calculus problems. When used for arithmetic operations, these devices help learners quickly confirm their answers for accuracy and build confidence in solving math problems.

Number Line

A number line is a simple yet effective visual tool that aids in understanding arithmetic operations, such as adding and subtracting integers. When dealing with negative numbers like in the problem \(-5 + (-9)\), it becomes particularly helpful. Here’s why:

• The number line represents all numbers, including negative, positive, and zero, in a straight line. Numbers to the left are negative, while those to the right are positive.
• When adding negative numbers, you can imagine moving leftwards from your starting point on the number line.
• For \(-5 + (-9)\), start at \(-5\) on the number line and move 9 steps to the left. This will land you at \(-14\).

Using a number line makes the concept of negative addition more tangible. It provides a clear picture of why adding two negative numbers results in an even more negative number, deepening the understanding behind integer operations.

Integer Operations

Integer operations, including addition and subtraction of whole numbers, form the basis of arithmetic calculations. When adding negative integers, such as \(-5 + (-9)\), a few simple rules help facilitate understanding.

• Adding a positive and a negative integer involves finding the difference and taking the sign of the larger absolute value. For instance, \(5 + (-9)\) results in \(-4\) because 9 is larger than 5.
• Adding two negative integers, results in adding their absolute values and retaining the negative sign. So, in \(-5 + (-9)\), it simply means combining \(5 + 9\) and appending the negative sign: \(-14\).
• Subtraction of a negative is equal to adding the corresponding positive number because a double negative makes a positive. Thus, \(-5 - (-9)\) becomes \(-5 + 9\).

Understanding these operations not only helps in tackling homework but also prepares students for more advanced topics involving integers in algebra and other branches of mathematics.