Problem 63 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \(-4+3(2-8)\)

Step-by-Step Solution

Answer

The result is \(-22\).

Step 1: Simplify inside the parenthesis

Start by simplifying the expression inside the parenthesis. Calculate the result of the operation inside, which is \(2-8\).

Step 2: Perform the subtraction

Calculate \(2 - 8\) to get \(-6\). Replace the parenthesis with \(-6\); the expression now becomes \(-4 + 3(-6)\).

Step 3: Multiply

Next, perform the multiplication. Multiply \(3\) by \(-6\), which results in \(-18\). The expression now is \(-4 - 18\).

Step 4: Perform the addition

Lastly, add \(-4\) and \(-18\). Adding two negative numbers gives a result of \(-22\).

Key Concepts

parentheses simplification

Simplifying expressions inside parentheses is crucial before performing any other arithmetic operations. Parentheses indicate that the operations enclosed should be executed first. For example, in the expression \(2-8\), start by subtracting 8 from 2.
Here’s how it looks:
\[2-8 = -6\]
Once simplified, replace the parentheses in the original expression with the result. Parentheses help ensure that the order of operations is maintained correctly. Without simplifying parentheses first, further steps would likely lead to incorrect results.

subtraction with negative numbers

Subtraction involving negative numbers can be tricky, so understanding the rules is essential. When subtracting a positive number from a smaller number, you cross zero, resulting in a negative number. For instance, \(2 - 8 = -6\).
Think of it as having 2 dollars and then owing 8 dollars more. The result is owing 6 dollars, hence -6.
Remember, subtracting a larger number from a smaller one always results in a negative number, indicating a deficit.

multiplication with negative numbers

Multiply negative numbers carefully to avoid mistakes. Remember these key rules for multiplication:

• Positive × Positive = Positive (\(4 \times 3 = 12\))
• Negative × Positive = Negative (\(-4 \times 3 = -12\))
• Positive × Negative = Negative (\(4 \times -3 = -12\))
• Negative × Negative = Positive (\(-4 \times -3 = 12\))

In our expression \(-4 + 3(-6)\), we multiply 3 by -6 resulting in -18. The rule applied here is Positive × Negative = Negative. This step transforms our expression to \(-4 - 18\).

addition of negative numbers

Adding negative numbers follows a simple rule: if both numbers are negative, the result remains negative. Think of negative numbers as money you owe. For example, owing 4 dollars and then owing 18 dollars more leaves you owing a total of 22 dollars. Mathematically, \(-4 + -18 = -22\).
To add negative numbers, simply add their absolute values (ignore the negative signs first) and then put a negative sign on the result. So for \(-4\) and \(-18\), add 4 and 18 to get 22, then apply the negative sign: \(-22\).