Problem 64 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \(-8+4(5-7)\)

Step-by-Step Solution

Answer

-16

Step 1 - Solve Inside the Parentheses

First, solve the expression inside the parentheses. Subtract 7 from 5: \[5 - 7 = -2\]

Step 2 - Multiply

Next, multiply the result from the parentheses by 4: \[4(-2) = -8\]

Step 3 - Add the Results

Finally, add -8 to -8: \[ -8 + (-8) = -16 \]

Key Concepts

Understanding Parentheses

When you see parentheses in a math problem, always perform the operations inside them first. Parentheses are like a protective bubble, where the operations inside must be completed before dealing with the rest of the equation.

For example, in the expression \(5 - 7\), you need to subtract 7 from 5. This operation results in -2.

Step-by-step:

• Solve \(5 - 7 = -2\)

This result then is used in the next steps of your overall problem.

The Role of Multiplication

Multiplication is an essential operation that often follows parentheses in math problems. Once parentheses are resolved, you multiply the result by the number outside the parentheses.

Using our exercise as an example, you take the answer from inside the parentheses, \(-2\), and multiply it by 4: \(4 \times (-2) = -8\).

Remember: Multiplication can change the sign of the result. For instance, multiplying a positive number by a negative number gives a negative result, as seen here: \(+4 \times -2 = -8\).

Adding the Results

Finally, addition can be performed once multiplication is complete. This step combines all the results you have so far.

In our problem, you are adding -8 (from the multiplication step) to -8 from the original problem. \( -8 + (-8) \) becomes \(-16\).

Key points to remember:

• Adding a negative number is the same as subtraction.
• Visualize the number line: starting at -8 and moving 8 spaces further left lands you at -16.

Thus, the final result of \(-8 + 4(5-7) = -16\).