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Chapter 1: Problem 64

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

Short Answer

Expert verified
-16

Step by step solution

01

- Solve Inside the Parentheses

First, solve the expression inside the parentheses. Subtract 7 from 5: \[5 - 7 = -2\]
02

- Multiply

Next, multiply the result from the parentheses by 4: \[4(-2) = -8\]
03

- Add the Results

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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 \(-8 + 4(5-7) = -16\).

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Most popular questions from this chapter

Use the distributive property to rewrite each expression. $$ 8(x-6) $$

Write a numerical expression for each phrase, and simplify the expression. The sum of \(\frac{1}{2}\) and \(\frac{5}{8},\) times the difference of \(\frac{3}{5}\) and \(\frac{1}{3}\)

Write a numerical expression for each phrase, and simplify the expression. The product of \(-\frac{1}{2}\) and \(\frac{3}{4},\) divided by \(-\frac{2}{3}\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 8 if its last three digits form a number divisible by \(8,\) and not otherwise. (a) Is 2,923,296 divisible by \(8 ?\) (b) Is 7,291,623 divisible by \(8 ?\)

Write a numerical expression for each phrase, and simplify the expression. 12 less than the difference of 8 and -5
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