Problem 11 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

-1

Step 1: Understand the Expression

We need to evaluate the expression \(x + 3\) by substituting the given value of \(x\).

Step 2: Substitute the Value

Substitute \(x = -4\) into the expression, which gives us \(-4 + 3\).

Step 3: Perform the Calculation

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

Key Concepts

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.