Problem 44 - Prealgebra

Question

Find the value of \(2 x+6\) when \(x=0\).

Step-by-Step Solution

Answer

The value of the expression is 6.

Step 1: Substitute the Value of x

Begin by substituting the provided value of \(x\) into the expression. Given \(x=0\), the expression becomes \(2 \times 0 + 6\).

Step 2: Simplify the Expression

Calculate the multiplication and then perform the addition. First, \(2 \times 0 = 0\), so the expression now is \(0 + 6\).

Step 3: Compute the Final Result

Add the results from the previous step. Thus, \(0 + 6 = 6\).

Key Concepts

Understanding Prealgebra Expressions

Prealgebra is one of the foundational math skills you will encounter in your journey as a student. It's all about understanding and working with basic mathematical expressions, which are combinations of numbers, variables, and arithmetic operations. Variables like "x" are often used as placeholders that can vary in value. When you see an expression such as \(2x + 6\), it might initially look confusing. However, it's just a way of saying "twice whatever x is plus six." Each element in an expression has a role, and your job is to find out what those elements say about the numbers involved. Expressions do not always have a specific value until variables are assigned specific values, which is where substitution comes in.

The Role of Arithmetic Operations in Expressions

Arithmetic operations are the basic computational skills that we use to manipulate numbers. The four fundamental arithmetic operations are addition, subtraction, multiplication, and division. When working with expressions, these operations tell you what to do with the numbers and variables. In the expression \(2x + 6\), multiplication occurs first because of the order of operations, which states that you handle multiplication before addition. Therefore, you multiply 2 by whatever "x" is before adding 6. This is an important step that ensures you're performing the operations in the correct sequence. Understanding how and when to apply these operations is crucial for solving expressions accurately.

How to Simplify Expressions

Simplifying expressions means doing as much arithmetic as possible to make them easier to work with. It involves carrying out operations in the right order—parentheses, exponents (if any), multiplication and division (from left to right), and addition and subtraction (from left to right). You might know this sequence of steps as PEMDAS/BODMAS. When you substitute a number into an expression, like replacing "x" with 0 in \(2x + 6\), you're on the first step to simplifying. Next, carry out the arithmetic within the expression. Calculate \(2 \times 0\) to get 0, and then add 6 to find the final value. Simplifying isn't just about crunching numbers; it's about ensuring every part of the expression is as compact as possible, making it quick and easy to evaluate.