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Chapter 1: Problem 13

Evaluate each following expression for \(x=2, y=5,\) and \(z=3 .\) \(4 x-z\)

Short Answer

Expert verified
The value of the expression is 5.

Step by step solution

01

Substitute the Variables

First, substitute the provided values into the expression. Given is the expression \(4x - z\), where \(x = 2\) and \(z = 3\). This substitution yields: \(4(2) - 3\).
02

Apply the Multiplication

Now perform the multiplication part of the expression. Calculate \(4 \times 2\) which equals \(8\). So the expression now is \(8 - 3\).
03

Perform the Subtraction

Finally, subtract \(3\) from \(8\). \(8 - 3 = 5\). This is the final result of the evaluation.

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Key Concepts

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

Substitution in Expressions
In algebra, substitution is a technique where we replace variables in an expression with provided numbers. This makes it easier to evaluate expressions and find the result.
For instance, if you have an expression like \(4x - z\), and are given the values \(x=2\) and \(z=3\), you substitute these values directly into the expression.
  • Replace \(x\) with 2, and \(z\) with 3.
  • Yielding the new expression: \(4(2) - 3\).
This substitution helps transform the algebraic expressions into arithmetic operations that are easy to compute. It is a crucial first step in solving many algebraic problems.
Order of Operations
When solving expressions that involve several operations, it is important to know the order in which to perform these operations. The order of operations is guided by the acronym PEMDAS:
  • P: Parentheses first
  • E: Exponents (i.e., powers and roots, etc.)
  • M/D: Multiplication and Division (left-to-right)
  • A/S: Addition and Subtraction (left-to-right)
This helps maintain consistency in solving expressions. In our example, after substitution, we have the expression \(4(2) - 3\).
Following PEMDAS, we first take care of the multiplication, performing \(4 \times 2\), before moving to subtraction. Performing operations in the correct order is vital to obtaining the correct answer.
Basic Arithmetic Operations
The basic arithmetic operations include addition, subtraction, multiplication, and division. Understanding these are fundamental to tackling algebraic expressions.
In our expression, \(4(2) - 3\), we use multiplication and subtraction:
  • Multiplication: Perform \(4 \times 2\) to get 8.
  • Subtraction: Then, subtract 3 from 8, resulting in 5.
Mastering these simple operations allows you to easily evaluate different expressions. They are the building blocks for understanding and working with more complex math problems.

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Most popular questions from this chapter

Match each word phrase to the correct translation. a. \(20 \div 200\) b. \(200 \div 20\) c. \(40 \div 8\) d. \(8 \div 40\) The quotient of 40 and 8.

Write each phrase as a variable expression. Use \(x\) to represent "a number." The sum of seventeen and a number added to the product of five and the number

Perform each indicated operation. $$ 47+26+10+231+50 $$

Use a calculator to evaluate each expression for \(x=23\) and \(y=72\). \(x^{2}+5 y-112\)

Use a calculator to evaluate each expression for \(x=23\) and \(y=72\). \(x^{4}-y^{2}\)
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