Problem 101 - Intermediate Algebra

Question

In the following exercises, simplify each expression. $$ 5(-6)+7(-2)-3 $$

Step-by-Step Solution

Answer

-47

Step 1: Multiply the Numbers Inside the Parentheses

First, multiply the numbers inside the parentheses: 5(-6) = -30 7(-2) = -14

Step 2: Substitute Results and Simplify

Replace the expressions inside the parentheses with their products and write down the simplified expression: -30 + -14 - 3

Step 3: Perform Addition and Subtraction

Add and subtract the numbers from left to right: -30 + -14 = -44 -44 - 3 = -47

Key Concepts

Multiplication

Let's start with multiplication, a fundamental arithmetic operation. Multiplication is repeated addition; for example, multiplying 3 by 4 means adding 3 four times: 3 + 3 + 3 + 3 = 12. In our exercise, we applied this concept by multiplying the given numbers inside the parentheses. When multiplying a positive number by a negative number, the result is negative. For instance, 5 times -6 equals -30 because we are adding -6 five times. Similarly, 7 times -2 equals -14 as we are adding -2 seven times. This step helps break down complex expressions into simpler parts.

Addition

Addition is another key arithmetic operation where we combine numbers to find their total. It's the process of calculating the sum of two or more numbers. In our exercise, once we replaced the expressions inside the parentheses with their products, we used addition to combine -30 and -14. Since both numbers are negative, their sum is more negative. Adding -30 and -14, we get -44. Remember, when adding two negative numbers, you add their absolute values and then apply the negative sign to the result.

Subtraction

Finally, let's discuss subtraction, which is taking one number away from another. This operation is essential for finding the difference between numbers. In the last step of our exercise, we subtracted 3 from -44. Subtraction is, in a way, the opposite of addition. When we subtract a positive number from a negative number, we increase the absolute value of the negative number. Hence, -44 minus 3 equals -47. Subtraction helps in reducing the value, making it smaller by the value being subtracted.