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Chapter 0: Problem 41

In Problems \(41-48\), evaluate each expression if \(x=-2\) and \(y=3\). \(x+2 y\)

Short Answer

Expert verified
The value of the expression is 4.

Step by step solution

01

- Identify given values

We are given the values of two variables: \(x = -2\) and \(y = 3\).
02

- Substitute given values into the expression

Take the expression \(x + 2y\) and substitute the given values: \(-2 + 2(3)\).
03

- Compute the multiplication

First, compute the multiplication part of the expression: \(2(3) = 6\).
04

- Perform the addition

Now, add the result from the multiplication to \(x\): \(-2 + 6\).
05

- Simplify the result

Simplify the expression: \(-2 + 6 = 4\).

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Key Concepts

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

Substitution
Substitution is a key concept in algebra where we replace variables with their given numerical values. Here, we know the values of two variables: \( x = -2 \) and \( y = 3 \). When asked to evaluate an expression like \( x + 2y \), we directly substitute these values into the expression. For instance, instead of \( x \), we use \( -2 \) and replace \( y \) with \( 3 \). Now, the expression transforms from \( x + 2y \) into \( -2 + 2(3) \). This makes the problem much more straightforward and allows us to use basic arithmetic operations to find the result.
Expression Simplification
Expression simplification is all about breaking down an algebraic expression into simpler terms or numbers. After substitution, the expression becomes \( -2 + 2(3) \). Here, we break it down further. Start by performing the multiplication operation first, as per the order of operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Compute \( 2(3) \) which equals \( 6 \).
Then, the expression reduces to \( -2 + 6 \). The simplified form makes it easier to perform the final addition and find the result.
Basic Arithmetic Operations
Basic arithmetic operations are the building blocks of mathematics. These include addition, subtraction, multiplication, and division. In this exercise, we see them in action. After substituting \( x = -2 \) and \( y = 3 \) into the expression \( x + 2y \), we got \( -2 + 2(3) \).
First, perform the multiplication \( 2(3) = 6 \).
Then, handle the addition: we add \( -2 \) and \( 6 \).
When adding negative and positive numbers, think of it like this: You are at \( -2 \) on a number line and you move 6 steps to the right. You end up at \( 4 \).
So, \( -2 + 6 = 4 \). And that's the final simplified answer.

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Most popular questions from this chapter

\text { In scientific notation, } 1234.5678= ________________

Write each statement using symbols. The product of 2 and \(x\) is the product of 4 and \(6 .\)

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Factor each polynomial completely. If the polynomial cannot be factored, say it is prime. $$ 1-8 x^{2}-9 x^{4} $$

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