Problem 70 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \((-9-4)(-2)+10\)

Step-by-Step Solution

Answer

36

Step 1: Simplify the Parentheses

First, simplify the expression inside the parentheses. For (-9 - 4), calculate -9 - 4 which equals -13. Therefore, the expression becomes (-13)(-2) + 10.

Step 2: Perform Multiplication

Next, perform the multiplication (-13)(-2). Recall that the product of two negative numbers is positive. Thus, (-13)(-2) equals 26. The expression now is 26 + 10.

Step 3: Perform Addition

Lastly, add the numbers. Calculating 26 + 10 gives 36.

Key Concepts

Simplify Expressions

In algebra, simplifying expressions is a key step to making calculations easier and more manageable. When simplifying expressions, you often begin by dealing with parentheses first. This is because operations inside parentheses are considered 'highest priority' and should be resolved before other operations.

For example, in the expression \((-9-4)(-2)+10\), you first need to simplify \((-9-4)\). Calculate -9 - 4, which equals -13. Your expression now looks like \((-13)(-2)+10\).

Remember:

• Simplify inside parentheses first
• Follow the Order of Operations (PEMDAS/BODMAS)

Multiplication of Negative Numbers

The multiplication of negative numbers follows some specific rules. If you multiply two negative numbers, the result is positive. This can sometimes be confusing, but here's a simple way to think about it: Two negatives make a positive.

Let's go back to our example: \((-13)(-2)+10\). To perform the multiplication, multiply -13 by -2.

So, we calculate:

• -13 \(\times\) -2 = 26

The expression now simplifies to 26 + 10.

Important points to remember:

• Negative \(\times\) Negative = Positive
• Negative \(\times\) Positive = Negative
• Positive \(\times\) Positive = Positive

Addition of Integers

Adding integers is one of the most basic operations in mathematics, but it’s still crucial to understand it clearly.

The general rule is to add the values directly if they share the same sign. If they have different signs, subtract the smaller absolute value from the larger one, and take the sign of the number with the larger absolute value.

Now, we take our simplified expression 26 + 10. Both are positive, so we add them directly:

• 26 + 10 = 36

Therefore, the final answer is 36.

Quick tips:

• Same sign: Add the numbers and keep the sign
• Different signs: Subtract smaller absolute value from larger, take larger's sign