Problem 11 Evaluate. $x+3,$ where \(x=-... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 2: Problem 11

Evaluate. $x+3,$ where $x=-4$

Short Answer

Expert verified

-1

Step by step solution

Understand the Expression

We need to evaluate the expression $x + 3$ by substituting the given value of $x$.

Substitute the Value

Substitute $x = -4$ into the expression, which gives us $-4 + 3$.

Perform the Calculation

Calculate $-4 + 3$. This is done by adding a positive and a negative number, which results in $-1$.

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Key Concepts

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

Substitution

Substitution in algebra involves replacing variables with their numerical values to simplify expressions and solve equations. The primary goal is to turn an algebraic expression into a simpler or solvable form.
In our exercise, the expression is initially given as $x + 3$. The problem provides the value of $x$ as $-4$. By substituting this value, the expression now becomes $-4 + 3$.
This step is fundamental in algebra, as it forms the basis for solving many types of equations. It's crucial to always substitute accurately to avoid errors and to always write down what you're substituting to keep track of your steps.

Negative Numbers

Negative numbers are numbers less than zero and are represented with a minus sign. They are used to represent values below a defined origin on the number line.
When dealing with negative numbers, their operations follow specific rules that sometimes differ from positive numbers. For example:

When adding a positive number to a negative number, you move towards the right on the number line.
If you are subtracting a negative number, it is equivalent to adding its positive counterpart.
Multiplying two negative numbers always results in a positive number.

In this example, we are adding a positive number to a negative number, $-4\ + 3$. This means you start at $-4$ on the number line and move three steps to the right, resulting in $-1$.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. They are the building blocks of mathematics and are used for both simple calculations and more complex algebraic manipulations.
In this exercise, the specific operation involved is addition where one number is negative. Remember the following rules for these operations:

Addition: Combine numbers; if they have different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value.
Subtraction: Controlled by adding the opposite; works similarly to addition but requires adjusting the sign of the second number.

Returning to our problem, the operation \-4\ + 3\ highlights the need to understand these rules. The result \-1\ shows how the positive $3$ decreases the absolute value of the negative $4$, resulting in a simple yet critical example of addition with negative numbers.

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91影视

Evaluate. \(x+3,\) where \(x=-4\)

Short Answer

Step by step solution

Understand the Expression

Substitute the Value

Perform the Calculation

Key Concepts

Substitution

Negative Numbers

Arithmetic Operations

One App. One Place for Learning.

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