Problem 63 Evaluate each expression for \(x... [FREE SOLUTION]

Chapter 2: Problem 63

Evaluate each expression for $x=-2, y=4,$ and $z=-1 .$ $$ 2 x-3 y-4 z $$

Short Answer

Expert verified

The value of the expression is -12.

Step by step solution

Substitute the Values

Replace each variable in the expression with the given values: $x = -2$, $y = 4$, and $z = -1$. This gives us the expression: $2(-2) - 3(4) - 4(-1)$.

Calculate Each Term

Compute the values for each term individually: $2(-2) = -4$, $-3(4) = -12$, and $-4(-1) = 4$.

Combine the Results

Add together the results from Step 2: $-4 - 12 + 4$.

Simplify the Expression

Simplify the combined terms: $-4 - 12 + 4 = -12$.

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Key Concepts

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

Substitution

Substitution is an essential skill in mathematics, especially when evaluating expressions. It involves replacing the variables in an equation with given values. This can turn a complex-looking expression into something more manageable.
In our example, we replaced the variables with the specified numbers:

For the variable $x$, we used $-2$.
For $y$, we substituted $4$.
Finally, for $z$, we replaced it with $-1$.

This turns the algebraic expression $2x - 3y - 4z$ into a numeric one: $2(-2) - 3(4) - 4(-1)$.
By substituting correctly, you set the stage for accurate arithmetic operations, leading to the right answer.

Arithmetic Operations

Arithmetic operations are the next step after substitution. They involve performing basic mathematical chores like addition, subtraction, multiplication, and division.
In our exercise, we have three main operations:

First, we multiply each number with its coefficient:
$2 \times -2 = -4$
$-3 \times 4 = -12$
$-4 \times -1 = 4$

Make sure to handle negative signs with care, as they can change the results significantly. Understanding how to accurately carry out arithmetic operations is vital as it ensures that each term contributes its true value to the final solution.
This phase is crucial for making sure each part of the expression is evaluated correctly.

Simplifying Expressions

After performing arithmetic operations, the next task is to simplify the expression by combining like terms. Simplification helps present a solution that is easy to interpret and understand.
In this problem, you gather the results of each term calculation:

$-4$
$-12$
$+4$

Simply add or subtract these to get to your final answer: $-4 - 12 + 4 = -12$.
Simplifying involves careful addition and subtraction, ensuring each step produces the correct intermediate result until you arrive at the expression鈥檚 simplest form.
Through simplification, complex problems become manageable, paving the way for clear solutions and deeper understanding.

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91影视

Evaluate each expression for \(x=-2, y=4,\) and \(z=-1 .\) $$ 2 x-3 y-4 z $$

Short Answer

Step by step solution

Substitute the Values

Calculate Each Term

Combine the Results

Simplify the Expression

Key Concepts

Substitution

Arithmetic Operations

Simplifying Expressions

One App. One Place for Learning.

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