Problem 68 Evaluate each expression for \(x... [FREE SOLUTION]

Chapter 2: Problem 68

Evaluate each expression for $x=-2, y=4,$ and $z=-1 .$ $$ \frac{4 x}{y} $$

Short Answer

Expert verified

The expression evaluates to $-2$.

Step by step solution

Substitute the Given Values into the Expression

Replace each variable in the expression $ \frac{4x}{y} $ with the corresponding values: $ x = -2 $ and $ y = 4 $. This gives us $ \frac{4(-2)}{4} $.

Simplify the Numerator

Calculate the product in the numerator. Multiply 4 by $ -2 $ to get $ -8 $. The expression now looks like $ \frac{-8}{4} $.

Divide the Numerator by the Denominator

Divide $ -8 $ by $ 4 $ to simplify the expression. The result is $ -2 $.

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Key Concepts

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

Substitution

Substitution in algebra is a fundamental skill and helps in solving expressions by replacing variables with their known values. This process involves a few simple steps.

Here鈥檚 how you can think of it:

First, identify which variables need to be replaced in the algebraic expression.
Next, replace each variable with its given value.
Ensure to perform this carefully to avoid any errors.

In our example, we started with the expression $ \frac{4x}{y} $. We need to replace $ x $ and $ y $ with $ -2 $ and $ 4 $ respectively. This step involves substituting each instance of $ x $ and $ y $ in the expression with the corresponding number.

This makes the expression $ \frac{4(-2)}{4} $, which is now ready for simplification. Substitution sets the stage for further calculations, making complex expressions easier to manage.

Simplification

After performing substitution, the next step is simplification. Simplification means reducing an expression to its most basic form.

Here's how you simplify:

First, address any operations within parentheses or involving multiplication/division.
Next, combine like terms or perform arithmetic operations.
Finally, look for common factors that can simplify fractions.

In our case, the expression became $ \frac{4(-2)}{4} $, after substitution.
Here, we simplify the expression by performing multiplication in the numerator: $ 4 \times (-2) $ equals $ -8 $. The expression then is transformed to $ \frac{-8}{4} $.

Simplification helps to turn complex-looking expressions into simpler, more understandable terms. It makes calculations easier and results clearer.

Fractions

Fractions often appear in algebra, especially when dealing with expressions or equations. Understanding fractions is key to simplifying and solving these expressions properly.

A fraction is made up of a numerator and a denominator:

The numerator is the top part of the fraction which signifies how many parts of a whole are being considered.
The denominator is the bottom part which represents the total number of equal parts the whole is divided into.

In our exercise, we have the fraction $ \frac{-8}{4} $. At this stage, simplifying the fraction involves dividing the numerator by the denominator.
Divide $ -8 $ by $ 4 $, which results in $ -2 $.

This calculation completes the evaluation of the expression. Working with fractions can sometimes seem tricky, but by systematically simplifying them, calculations can become straightforward.

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91影视

Evaluate each expression for \(x=-2, y=4,\) and \(z=-1 .\) $$ \frac{4 x}{y} $$

Short Answer

Step by step solution

Substitute the Given Values into the Expression

Simplify the Numerator

Divide the Numerator by the Denominator

Key Concepts

Substitution

Simplification

Fractions

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