/*! 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 51 Evaluate each expression when \(... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 51

Evaluate each expression when \(x=1, y=3,\) and \(z=5.\) \(3 x-2\)

Short Answer

Expert verified
The expression evaluates to 1.

Step by step solution

01

Substitute the values

Replace the variable in the expression with its corresponding value. In this expression, substitute \(x\) with 1. Thus, the expression \(3x - 2\) becomes \(3(1) - 2\).
02

Calculate the multiplication

Perform the multiplication operation. In this case, multiply 3 and 1. This gives us \(3 \times 1 = 3\).
03

Subtract to find the result

Subtract 2 from the result of the multiplication. This is calculated as \(3 - 2 = 1\).

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.

Substitution Method
The substitution method is a fundamental concept in algebra used to replace variables with given numerical values. This approach simplifies expressions and aids in solving equations. For instance, in the algebraic expression presented, we replace the variable \(x\) with a number provided, which is 1. This is like filling in the blank with the correct number.
  • Identify the expressions that contain variables.
  • Replace each variable with its corresponding value.
  • This method can be helpful in simplifying expressions or solving equations.
Using substitution helps make abstract numerical relationships concrete by converting expressions into arithmetic calculations.
Algebraic Expressions
Algebraic expressions are mathematical statements that include variables, numbers, and operation symbols (like addition, subtraction, multiplication, etc.). These expressions represent relationships between numbers.
In our case, the expression is \(3x - 2\). The variable \(x\) is multiplied by 3 and then reduced by 2.
  • Variables: Stand-in symbols that can represent unknown or variable quantities.
  • Coefficients: Numbers that multiply variables (like 3 in \(3x\)).
  • Constants: Numbers that stand alone (like the -2).
Understanding how to manipulate these expressions is crucial for solving algebraic problems efficiently.
Order of Operations
The order of operations is a set of rules outlining the sequence to follow when evaluating mathematical expressions. Remembering this sequence helps avoid mistakes when dealing with complex expressions.A common acronym, PEMDAS, stands for:
  • Parentheses: Complete calculations inside parentheses first.
  • Exponents: Evaluate exponents next.
  • Multiplication and Division: Process these from left to right.
  • Addition and Subtraction: Lastly, perform these operations from left to right.
In the expression \(3x - 2\), once the substitution is done, you first handle the multiplication (3 times 1) and then perform the subtraction (minus 2) following the order prescribed by PEMDAS. This prioritization ensures accuracy in simplifying and solving problems.

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

Simplify each expression. (Remember the order of operations.) See Examples 4 and 5. $$ (3-6)+4^{2} $$

Perform the following operations. Write answers in lowest terms. $$ 1 \frac{1}{2}+3 \frac{2}{3} $$

Fill in the table with the opposite (additive inverse), and the reciprocal (multiplicative inverse). Assume that the value of each expression is not 0 $$ \frac{1}{2 x} $$

Perform the following operations. Write answers in lowest terms. $$ \frac{2}{3}+\frac{3}{5} $$

Simplify each expression. (Remember the order of operations.) See Examples 4 and 5. $$ -2+[(8-11)-(-2-9)] $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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.