Problem 61 Evaluate each expression for \(x... [FREE SOLUTION]

Chapter 2: Problem 61

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

Short Answer

Expert verified

The expression evaluates to 1.

Step by step solution

Substitute the values

First, we substitute the given values for the variables into the expression. So replace $x$ with $-2$, $y$ with $4$, and $z$ with $-1$. The expression becomes: $-2 + 4 + (-1)$.

Simplify the expression

Now, calculate the result by simplifying the expression from left to right. First, compute $-2 + 4 = 2$. Then, add the result to $-1$: \[2 + (-1) = 1\].

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Key Concepts

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

Substitution

Substitution is like changing clothes for variables. In math, we replace symbols with actual numbers.
This step is crucial when evaluating expressions.Let's clarify with an example. Suppose you have an expression like $x + y + z$. If we are given that $x = -2$, $y = 4$, and $z = -1$, substitution means replacing each letter with its value.

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

After substitution, our expression $x + y + z$ transforms into $-2 + 4 + (-1)$. This new form can now be simplified.

Simplification

Simplification involves breaking down expressions into simpler forms. It's like tidying up the math work to see the answer clearly.
After substitution, we often get an expression with numbers that can be combined.In our example, the expression is $-2 + 4 + (-1)$. To simplify, perform the operations step-by-step:

Begin with the leftmost numbers: calculate $-2 + 4$. This gives us $2$.
Take this result and combine it with the next number: $2 + (-1)$.

After combining, you find that the expression simplifies to $1$. Each operation brings us closer to the final result.

Integer Operations

Integer operations include addition, subtraction, multiplication, and division with whole numbers. Understanding these operations helps in simplifying expressions.
When working with integers, especially negative ones, you need to be careful with how signs are handled.In our example, we performed addition:

First with $-2 + 4$, which involves adding a negative and a positive integer.
Then with $2 + (-1)$, which again involves combining positive and negative values.

Consider the rules: - Adding a positive number moves towards higher values (right on the number line).- Adding a negative number moves towards lower values (left on the number line).Recognizing these rules helps ensure accurate results when evaluating expressions with integers.

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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

Substitute the values

Simplify the expression

Key Concepts

Substitution

Simplification

Integer Operations

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