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Chapter 1: Problem 79

Evaluate the expression for the given value of the variable. $$7 \text {x when} \quad x=3$$

Short Answer

Expert verified
The value of the expression when \(x=3\) is 21

Step by step solution

01

Identification of the Expression and Variable

Firstly, identify the given expression and variable. The given expression in this exercise is \(7x\) and the variable \(x\) is given the value 3.
02

Substitute Variable Value into the Expression

Now, substitute the given value of the variable \(x\) into the expression. This will result in the mathematical operation \(7 * 3\).
03

Evaluate the Result

After substitution, the last step is to simplify the equation. The multiplication \(7 * 3\) equals 21.

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Key Concepts

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

Understanding Substitution
Substitution is the process of replacing variables in an expression with specific values. This process is crucial in algebraic calculations. Imagine you have a mystery box labeled "x" and you're told what the box contains. In this case, the box labeled "x" contains the number 3. In algebraic terms, you substitute the variable "x" with "3" in its place within the expression.

By doing so, you transform the expression from its generic form to one that can actually be calculated. When working with expression substitutions, it's essential to ensure clarity and accuracy. Incorrect substitution could lead to wrong results. Remember:
  • Identify the parts of the expression needing substitution.
  • Double-check the value of the variable you are given.
  • Place the value in all locations of the variable within the expression.
The Role of Variables
Variables might seem daunting, but they're actually quite simple. In algebra, a variable is often represented by a letter, like "x", "y", or "z". These letters stand in for unknown values or numbers that aren't yet known. They play a vital role in forming an expression or equation.

Variables allow flexibility since they can take on any value. When you're tasked to evaluate a mathematical expression, one of your first moves is to determine what each variable stands for. This exercise provided that the variable "x" equals 3. Understanding variables involves:
  • Recognizing what the letter represents.
  • Keeping track of their assigned values.
  • Replacing them accurately for precise calculation results.
Basics of Multiplication
Multiplication is a mathematical operation that combines numbers in a way that associates them into a group. When you multiply, you essentially add a number to itself a certain number of times. In the context of our exercise, you have to multiply 7 by 3, which means you add 7 to itself three times.

The act of multiplication simplifies repeated addition, making calculations faster and more efficient. Here's how to view multiplication in a practical sense:
  • Recognize it as a shortcut to repeated addition.
  • Be precise with your multiplication factors.
  • Always double-check your result, especially in larger expressions.

Accurate multiplication is essential for any subsequent steps in solving algebraic expressions, as it forms the basis for simplifying and reaching the final solution.

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Most popular questions from this chapter

Evaluate the expression for the given value of the variable. (Review 1.2) $$4\left(t^{3}\right) \text { when } t=3$$

Evaluate the expression. $$\frac{1}{3}(9 \cdot 3)+18$$

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) A piece of cheese cut in the shape of a cube has a volume of 27 cubic inches. What is the length of each edge of the piece of cheese?

The area A of a trapezoid with parallel bases of lengths \(b_{1}\) and \(b_{2}\) and height \(h\) is \(A=\frac{1}{2} h\left(b_{1}+b_{2}\right)\) Find the area of a trapezoid whose height is 2 meters and whose bases are 6 meters and 10 meters. (GRAPH CANNOT COPY)

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$a(3 a+2)>50 ; 4$$
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