Problem 72 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \(4(-8)+|4-15|\)

Step-by-Step Solution

Answer

-21

Step 1: Multiply

Perform the multiplication operation first. Multiply 4 by -8 to get -32. So, the expression is now \[-32 + |4 - 15|\].

Step 2: Calculate Absolute Value

Next, find the absolute value of 4 - 15. Subtract 15 from 4 to get -11. The absolute value of -11 is 11. So, the expression is now \[-32 + 11\].

Step 3: Add the Results

Finally, add the two results together: -32 + 11. This sums to -21.

Key Concepts

Multiplication

Multiplication is one of the basic arithmetic operations where we find the total of one number being added a certain number of times.
In algebraic expressions, multiplication often plays a crucial role.
Let's look at our initial step from the problem: we had to multiply 4 by -8.

To multiply two numbers:

• First, remember the rule for multiplying positive and negative numbers: a positive times a negative gives a negative.
• So here, multiplying 4 (positive) by -8 (negative) results in -32.

The expression transformed from 4(-8) + |4 - 15| to -32 + |4 - 15|.

Absolute Value

The absolute value of a number is its distance from zero on the number line, without considering which direction.
This means it's always a non-negative number, even if the original number is negative.
Absolute value is represented by two vertical bars: | |.

In our problem, we had to find the absolute value of 4 - 15.

• First, subtract 15 from 4 to get -11.
• Second, apply the absolute value rules: the absolute value of -11 is 11 (because you're counting the distance from zero).

So, the expression goes from -32 + |4 - 15| to -32 + 11.

Addition

Addition is another fundamental arithmetic operation where we find the total of two or more numbers.
When dealing with addition in algebra, make sure to combine like terms and consider the signs of the numbers:

• Positive numbers increase the total.
• Negative numbers decrease the total.

In our final step from the problem, we needed to add -32 and 11.

• Since -32 is negative and 11 is positive, combining them is like subtracting 11 from 32 but keeping the sign of the larger number (which is negative in this case).
• Subtracting 11 from 32 gives us 21.
• Applying the sign of the larger number, we end up with -21.

Thus, the final result of the expression is -21.