Problem 51 - Elementary and Intermediate Algebra

Question

Simplify. $$ 8(-7)+|6(-5)| $$

Step-by-Step Solution

Answer

-26

Step 1: Multiply Inside the Parentheses

Start by performing the multiplication inside the parentheses. First, calculate the product inside the first parentheses: \( 8(-7) = -56 \)

Step 2: Evaluate the Absolute Value Expression

Next, calculate the product inside the absolute value: \( 6(-5) = -30 \) Then, take the absolute value of the result: \( |-30| = 30 \)

Step 3: Add the Results

Now add the results from Step 1 and Step 2: \( -56 + 30 = -26 \)

Key Concepts

Simplifying expressions

Simplifying expressions means to reduce them to their simplest form. The goal is to make the expression easier to understand and work with.

Here’s how you do it step-by-step:

• Identify and perform operations within parentheses.
• Evaluate any absolute values.
• Combine like terms and perform any remaining arithmetic operations.

In the given exercise, we start by simplifying the multiplications within the parentheses. This is the first step towards simplifying the entire expression.

Multiplication

Multiplication is one of the basic operations in mathematics where you combine equal groups together.

In the context of our exercise, we multiply numbers inside the parentheses. For example, multiplying 8 by -7, and 6 by -5.

• For the first part: \( 8(-7) = -56 \)
• For the second part inside the absolute value: \( 6(-5) = -30 \)

Remember that multiplying two numbers with different signs (positive and negative) results in a negative number.

Absolute value

Absolute value represents the distance a number is from zero on a number line, without considering direction.

In simpler terms, it always results in a non-negative number. If the number inside the absolute value is negative, we convert it to positive.

In our problem:

• First, we find the product: \( 6(-5) = -30 \).
• Then, we convert to absolute value: \( |-30| = 30 \).

No matter how complex the expression inside the absolute value, the result will always be positive non-negative.

Addition

Addition is the process of bringing two or more numbers (or terms) together to make a new total.

In the final step of our exercise, we add the results from the simplification and absolute value steps.

Adding \(-56\) and 30 looks like this:

• \( -56 + 30 = -26 \)

When adding a negative number and a positive number, you essentially perform subtraction and keep the sign of the larger absolute value number.