Problem 20 By what number is it necessary t... [FREE SOLUTION]

91影视

Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 2: Problem 20

By what number is it necessary to divide both sides of each equation to isolate $x$ on the left side? Do not actually solve. $$ -x=50 $$

Short Answer

Expert verified

Divide both sides by -1.

Step by step solution

Identify the coefficient of x

In the given equation $-x = 50$, the coefficient of $x$ is $-1$.

Determine the necessary division

To isolate $x$, divide both sides of the equation by $-1$.

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Key Concepts

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

coefficients

In many algebraic equations, the coefficient is a crucial part of understanding and solving for a variable. A coefficient is the number that is directly multiplied by the variable. For instance, in the equation $-x=50$, we observe that the coefficient of $x$ is $-1$. This simply means that $x$ is being multiplied by $-1$. Recognizing coefficients helps us decide the operations needed to isolate the variable.

equation manipulation

Manipulating equations involves a series of steps to isolate the variable and solve the equation. Let鈥檚 break down the process:
- Identify the variable you need to isolate (in this case, $-x$).
- Identify the coefficient attached to the variable.
- Use inverse operations to isolate the variable.
For our specific exercise, the variable is $x$ and its coefficient is $-1$. To isolate $x$, we use the inverse operation, which leads us to the next section.

division

Division is a fundamental operation used to solve equations, especially when isolating a variable. It is the correct tool to 'undo' multiplication. In our example, because $x$ is multiplied by $-1$, we divide both sides of the equation by $-1$ to isolate $x$. For example:
- Given $-x=50$.
- Divide both sides by $-1$, leading to $\frac{-x}{-1} = \frac{50}{-1}$.
- This simplifies to $x = -50$.
By applying division correctly, we effectively isolate $x$ on one side of the equation, providing a clear solution.

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91影视

By what number is it necessary to divide both sides of each equation to isolate \(x\) on the left side? Do not actually solve. $$ -x=50 $$

Short Answer

Step by step solution

Identify the coefficient of x

Determine the necessary division

Key Concepts

coefficients

equation manipulation

division

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