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Chapter 1: Problem 57

Perform each indicated operation. \(-2(5)-(-4)(2)\)

Short Answer

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Step by step solution

01

- Distribute the Multiplication

First, distribute the multiplication within the parentheses. Calculate ewline \[\begin{equation} -2 \times 5 \text{ and } -(-4) \times 2 ewline -2 \times 5 = -10 ewline -(-4) \times 2 = 4 \times 2 = 8 \end{equation}\]
02

- Combine Results

Next, combine the results from the previous step. Calculate: \[\begin{equation} -10 + 8 = -2 \end{equation}\]

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Key Concepts

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

Multiplication of Integers
Understanding the multiplication of integers is crucial for solving mathematical problems efficiently. Here's a breakdown:

If you multiply two positive integers, the result is positive. For example:
\(3 \times 4 = 12\).

When you multiply a positive integer by a negative integer, the result is negative:
\(3 \times -4 = -12\).

Multiplying two negative integers gives a positive result:
\(-3 \times -4 = 12\).

Remember, the signs of the integers play a significant role:
  • Positive 脳 Positive = Positive
  • Positive 脳 Negative = Negative
  • Negative 脳 Negative = Positive
In the given exercise, we have:
\(-2 \times 5 = -10\)
\(-(-4) \times 2 = 4 \times 2 = 8\).
This explains why the signs of the integers impact the final results.
Distributive Property
The distributive property is a fundamental algebraic principle that simplifies expressions and equations. The property states:
\(a(b + c) = ab + ac\).
Take the problem we have: \(-2(5) - (-4)(2)\).
The steps taken can be broken down as follows:

**Step 1:** Distribute the multiplication within each parenthesis:
\( -2 \times 5 \) and \(-(-4) \times 2\).

This simplification involves basic multiplication first:
\(-2 \times 5 = -10\).
For \(-(-4) \times 2\), remember that \-(-4)\ becomes positive 4, leading to:
\(4 \times 2 = 8\).
Here, the distributive property helps manage and simplify expressions, preparing them for further mathematical operations.
Combining Like Terms
Combining like terms is the process to simplify expressions and equations by summing up terms that are similar. In algebra, like terms are terms that have the same variables raised to the same power. For instance:
  • \(3x + 5x\) can be combined to \((3+5)x = 8x\).
  • \(2y - y = y\).
In our problem, combining results after distributing the numbers:
We have \(-10 + 8\).
Here, \(-10\) and \(8\) are numbers (or constants), and can be combined directly:
\

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Most popular questions from this chapter

Write a numerical expression for each phrase, and simplify the expression. The product of -9 and \(2,\) added to 9

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\left(\frac{1}{3} x-\frac{4}{5} y\right)\left(-\frac{1}{5} a\right)\)

Solve each problem. Marcial owes \(\$ 679.00\) on his Visa account. He returns three items costing \(\$ 36.89, \$ 29.40\), and \(\$ 113.55\) and receives credit for these on the account. Next, he makes purchases of \(\$ 135.78\) and \(\$ 412.88\) and two purchases of \(\$ 20.00\) each. He makes a payment of \(\$ 400\). He then incurs a finance charge of \(\$ 24.57 .\) How much does he still owe?

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 6 if it is divisible by both 2 and \(3,\) and not otherwise. (a) Is 1,524,822 divisible by \(6 ?\) (b) Is 2,873,590 divisible by \(6 ?\)

Write a numerical expression for each phrase, and simplify the expression. 14 added to the sum of -19 and -4
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