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Chapter 4: Problem 47

Simplify. What must be added to \(-4 x\) to get a sum of \(0 ?\)

Short Answer

Expert verified
4 x must be added to -4 x to get a sum of 0.

Step by step solution

01

- Understand the Problem

The question asks what must be added to -4x to get a sum of 0 . This means finding a value that when added to -4 x equals zero.
02

- Set up the Equation

Set up the equation -4 x + ? = 0 . Here, the question mark represents the value that needs to be added to -4 x .
03

- Solve the Equation

To find the value that needs to be added, isolate the question mark by adding 4 x to both sides of the equation. -4 x + 4 x = 0 + 4 x 0 (result of left-hand side) = 4 x(result of right-hand side) This simplifies to ? = 4x .

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Key Concepts

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

simplifying expressions
Simplifying expressions is a core task in algebra. It involves reducing expressions to their simplest form without changing their values. To do this, you often combine like terms or use basic arithmetic operations. In the given exercise, the expression \( -4x \) needs to be manipulated 馃М. You identify what should be added to \( -4x \) to reach zero. By understanding the expression's components and systematically simplifying it, you can find the solution effortlessly.
solving equations
Solving equations involves finding the values of unknown variables that make the equation true. The exercise requires setting up an equation from \( -4x + ? = 0 \). This equation equates the sum of \( -4x \) and an unknown value to zero. By isolating the unknown variable, we reveal the solution. Here, moving \( -4x \) to the other side changes the equation to \( ? = 4x \), solving it efficiently 馃搳.
inverse operations
Inverse operations are operations that undo each other. Addition and subtraction are inverse operations, as are multiplication and division. To solve \( -4x + ? = 0 \), you add \( 4x \) to both sides. This demonstrates how adding is used to neutralize the subtraction of \( 4x \). Recognizing which operation to use helps in simplifying and solving equations 馃攧. The equation thus transforms into \( 0 = 4x \), and finally \( ? = 4x \).
addition property of equality
The addition property of equality states that adding the same value to both sides of an equation keeps the equation balanced. In the example, \(-4x + ? = 0\), we add \( 4x \) to both sides. This helps to isolate the unknown, simplifying the equation 馃搻. So, on adding \( 4x \) to each side, you get \( 0 = 4x \), showing that applying the addition property correctly leads to \( ? = 4x \). Thus, the unknown value needed to make \( -4x \) equal to zero is \( 4x \).

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Most popular questions from this chapter

Solve each system by substitution. Then graph both lines in the standard viewing window of a graphing calculator, and use the intersection feature to support your answer. $$ \begin{aligned} &y=6-x\\\ &y=2 x \end{aligned} $$

System of linear equations can be used to model the cost and the revenue of a business. Suppose that you start a business manufacturing and selling bicycles, and it costs you \(\$ 5000\) to get started. Each bicycle will cost \(\$ 400\) to manufacture. Explain why the linear equation $$ y_{1}=400 x+5000 \quad( \lefty_{1}\text { in dollars) }\right. \(gives your total cost of manufacturing \)x$ bicycles.

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