Problem 86 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. $$ |-4+8|+|6-1| $$

Step-by-Step Solution

Answer

9

Step 1 - Evaluate inside the first absolute value

Calculate o o compute inside the first absolute value: |-4 + 8|. Start by adding -4 and 8, which gives 4.

Step 2 - Apply the first absolute value

Next, find the absolute value of 4. Since 4 is already positive, the absolute value remains 4.

Step 3 - Evaluate inside the second absolute value

Calculate inside the second absolute value: |6 - 1|. Start by subtracting 1 from 6, which gives 5.

Step 4 - Apply the second absolute value

Next, find the absolute value of 5. Since 5 is already positive, the absolute value remains 5.

Step 5 - Add the results

Add the results of both absolute values: 4 + 5 which gives 9.

Key Concepts

absolute value

Absolute value represents the distance of a number from zero on the number line. This distance is always a non-negative value. For instance, the absolute value of -4 is 4, written as \(|-4| = 4\). Similarly, the absolute value of 5 is just 5, written as \(|5| = 5\). Understanding absolute value is crucial for solving many mathematical problems, including the one we'll discuss here.

basic arithmetic

Basic arithmetic includes fundamental operations such as addition and subtraction. These are foundational skills required for solving more complex math problems. In our exercise, we need to add and subtract numbers to find the values inside the absolute value bars. For example, inside \(|-4 + 8|\), we perform the addition \(-4 + 8 = 4\), and inside \(|6 - 1|\), we perform the subtraction \(6 - 1 = 5\). Mastering these basic operations simplifies the process of finding solutions.

step-by-step solutions

A step-by-step solution methodically breaks down a problem into manageable parts. This approach helps students understand each part of the problem before moving to the next. We used a step-by-step approach to solve the exercise as follows:

• First, evaluate inside each absolute value. For \(|-4 + 8|\), compute \(-4 + 8 = 4\).
• Then, apply the absolute value function. Here, \(|4| = 4\).
• Next, evaluate inside the second absolute value. For \(|6 - 1|\), compute \((6 - 1 = 5)\).
• Apply the absolute value function. Here, \(|5| = 5\).
• Finally, add the results of both absolute values: \(4 + 5 = 9\).

performing operations

Performing operations involves executing actions like addition, subtraction, multiplication, or division according to mathematical rules. In our exercise, we see this in action when evaluating expressions inside the absolute value bars. For \(|-4 + 8|\), perform the addition inside first to get 4. For \(|6 - 1|\), perform the subtraction inside first to get 5. After calculating the operations inside, we finally add the results of both absolute values (4 and 5) to get the final answer of 9.