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Chapter 1: Problem 12

Evaluate the variable expression when \(k=3\) $$ 7 k $$

Short Answer

Expert verified
The result of evaluating the expression \(7k\) when \(k=3\) is 21.

Step by step solution

01

Identify the variable and its given value

In the exercise, the variable \(k\) is given and it is specified that \(k=3\).
02

Substitute the given value into the expression

Substitute \(k=3\) into the expression \(7k\) to get \(7(3)\).
03

Compute the result

Now perform the multiplication operation to get the result of the expression. Calculate \(7*3\) which equals 21.

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Key Concepts

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

Substitution in Algebra
Understanding how to apply substitution in algebra is fundamental to solving mathematical problems entailing variables. During substitution, a given value replaces a variable within an expression.

Here is a step-by-step process of applying substitution:
  1. Identify the variable: Determine what letter or symbol is being used to represent the unknown value in the expression. In our example, the variable is k.
  2. Determine the value to substitute: Look for the value that the variable should be replaced with. In this case, k is replaced with the number 3.
  3. Execute the substitution: Replace every instance of the variable in the expression with the value. Following our example, wherever you see k, you would substitute it with 3 to get 7*3.
By making these replacements before you perform any calculations, you can greatly simplify algebraic expressions and make them easier to solve.
Algebraic Expressions
An algebraic expression is a combination of numbers, variables, and operation symbols that represents a specific quantity. Operations can include addition, subtraction, multiplication, division, and exponentiation. Unlike equations, algebraic expressions do not have an equal sign.

Components of an algebraic expression:
  • Terms: The different parts of an algebraic expression separated by + or - signs.
  • Coefficients: Numerical or constant factors of terms. In the example expression 7k, 7 is the coefficient.
  • Variables: Symbols that stand in place of unknown numbers. Here, k is the variable.
To evaluate an algebraic expression, you must substitute each variable with its corresponding value and perform the indicated operations.
Basic Algebra Operations
There are basic algebra operations that one must be familiar with in order to effectively evaluate algebraic expressions. These operations are addition, subtraction, multiplication, and division, and they are used to manipulate expressions.

When dealing with simple expressions like 7k, multiplication comes into play:
  1. Multiplication: This operation combines multiples of a number. For a variable expression, it often indicates repeated addition of that variable's value. If you have 7k and k is substituted with 3, then it means you are adding the value of 3 together, seven times.
  2. Order of Operations: Remember to follow the proper order of operations (PEMDAS/BODMAS) in more complex expressions. It stands for Parentheses/Brackets, Exponents/Orders, Multiplication, Division, Addition, and Subtraction.
By mastering these basic operations, you will be able to solve not only variable expressions but tackle more intricate algebraic problems as well.

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