Problem 62 Evaluate each expression for \(x... [FREE SOLUTION]

Chapter 2: Problem 62

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

Short Answer

Expert verified

The expression evaluates to -5.

Step by step solution

Identifying Values and Expression

First, identify the given expression: \[ x - y - z \].Also, note the values: $ x = -2 $, $ y = 4 $, and $ z = -1 $. We'll substitute these values into the expression.

Substituting Values

Replace the variables in the expression with their given values. This turns the expression $ x - y - z $ into:\[-2 - 4 - (-1)\].

Simplifying the Expression

Now, simplify the expression step-by-step:1. Simplify the first part: $-2 - 4 = -6 $.2. Simplifying further, consider the subtraction of a negative: $-6 - (-1) = -6 + 1 = -5$.

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Key Concepts

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

Evaluating Expressions

Evaluating expressions in prealgebra involves replacing variables with actual numbers and then performing the operations to find a single numerical result. This exercise starts with the expression $x - y - z$, where you need to substitute values for each variable to evaluate the expression.

To evaluate, replace each variable in the expression with their given values:

Let $ x = -2 $
Let $ y = 4 $
Let $ z = -1 $

Once the values are substituted, you'll perform the arithmetic operations which consist of subtraction in this particular expression.

This process of evaluating is fundamental as it shows how algebraic expressions can be translated into real numbers by simply following basic arithmetic rules.

Substitution Method

The substitution method is a key approach in algebra for finding the value of expressions by replacing variables with known values. Here, the original expression is $x - y - z$. This shows you will replace each variable with appropriate numbers:

Substitute $x$ with $-2$
Substitute $y$ with $4$
Substitute $z$ with $-1$

After substitution, the expression turns into $-2 - 4 - (-1)$.

This method ensures that variables, which are placeholders, have specific values that can then let you perform typical mathematical operations. Substitution streamlines the process of moving from symbolic manipulations to numeric calculations.

Simplifying Expressions

Simplifying expressions means reducing them to their simplest form by performing all possible operations. In this exercise, the goal is to take the expression $-2 - 4 - (-1)$ and find its simplest form.

Start by performing the subtraction operations step-by-step:

Begin with $-2 - 4$, which equals $-6$.
Then simplify the expression further: taking $-6 - (-1)$. Here, subtracting a negative is equivalent to adding a positive, so it becomes $-6 + 1$, which equals $-5$.

Simplifying involves not just applying arithmetic but understanding the rules that govern operations, such as how subtracting a negative can transform into addition. By simplifying, you find the expression's most reduced form, which is essential for clear and concise results.

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91影视

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

Short Answer

Step by step solution

Identifying Values and Expression

Substituting Values

Simplifying the Expression

Key Concepts

Evaluating Expressions

Substitution Method

Simplifying Expressions

One App. One Place for Learning.

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