/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 26 Evaluate each following expressi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 26

Evaluate each following expression for \(x=2, y=5,\) and \(z=3 .\) \(\frac{6+3 x}{z}\)

Short Answer

Expert verified
The expression evaluates to 4.

Step by step solution

01

Substitute the given values into the expression

Start by substituting the given values of \(x=2\), \(y=5\), and \(z=3\) into the expression \(\frac{6+3x}{z}\). This makes the expression \(\frac{6+3(2)}{3}\).
02

Simplify the Numerator

Calculate the expression in the numerator of the fraction. Substitute \(x = 2\) into the numerator: \(6 + 3(2) = 6 + 6 = 12\).
03

Perform Division

Divide the result of the numerator by \(z\), which is 3. So, \(\frac{12}{3} = 4\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Evaluating Expressions
Evaluating expressions involves calculating the value of a mathematical phrase by performing operations on given numbers. In our exercise, we have the expression \( \frac{6+3x}{z} \). To evaluate this, follow these steps:
  • Identify the variables and their assigned values (here, \( x=2 \), \( y=5 \), and \( z=3 \)).
  • Substitute these values into the expression in the respective places.
  • Simplify the expression using basic arithmetic operations like addition and division.
By replacing variables with their numerical values, you turn an abstract expression into a concrete number. This process can be used in diverse mathematical problems, allowing you to find specific solutions.
Numerical Substitution
Numerical substitution is often the first step in evaluating expressions. This method involves replacing variables in an expression with actual numerical values. Let's break this down using the given problem:
  • We start with the expression \( \frac{6+3x}{z} \).
  • Replace \( x \) with 2 and \( z \) with 3, resulting in the expression \( \frac{6+3(2)}{3} \).
After substituting, the expression is no longer a combination of variables, but a straightforward arithmetic problem. This makes it easier to simplify and solve, ensuring clarity and precision in your calculations.Numerical substitution is a foundational skill in algebra that helps bridge the gap from abstract expressions to tangible results.
Prealgebra Concepts
Prealgebra is all about understanding fundamental mathematical operations and how they interact in algebraic contexts. A primary concept is substitution and simplification:
  • Substitution involves replacing variables with values, turning complex expressions into simpler arithmetic.
  • Once substituted, you apply arithmetic operations such as addition and division to simplify further.
In the provided exercise, starting with a fraction like \( \frac{6+3x}{z} \) and substituting given values highlights how prealgebra strategies manage operations step by step.These concepts form the building blocks for more advanced algebra, helping to ensure that students can approach problems methodically. Mastery of prealgebra techniques is essential for progressing in mathematics, as it develops a strong foundation upon which more complex topics can be understood.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In your own words, explain how to round 9660 to the nearest thousand.

Identify each answer as correct or incorrect. Use addition to check. If the answer is incorrect, write the correct answer. $$ \begin{array}{r} 741 \\ -56 \\ \hline 675 \end{array} $$

Perform each indicated operation. $$ \begin{array}{r} 128 \\ +\quad 7 \\ \hline \end{array} $$

Write each whole number in expanded form. $$3470$$

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.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.