/*! 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 71 Evaluate each expression for the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 71

Evaluate each expression for the given values. \(5 a-2 b\) if \(a=4\) and \(b=3\)

Short Answer

Expert verified
The expression evaluates to 14.

Step by step solution

01

Substitute Given Values

Replace the variables in the expression with the given values. For the expression \(5a - 2b\), substitute \(a = 4\) and \(b = 3\). This results in \(5(4) - 2(3)\).
02

Multiply and Simplify

Perform the multiplication in the expression. Calculate \(5 \times 4 = 20\) and \(2 \times 3 = 6\). The expression now becomes \(20 - 6\).
03

Subtract to Find Final Answer

Subtract the results to find the final answer. Evaluate \(20 - 6\), which equals \(14\).

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
Substitution is a fundamental step in solving algebraic expressions. It involves replacing variables in an expression with the values provided. Let's consider the expression \(5a - 2b\). If we know that \(a = 4\) and \(b = 3\), we substitute these values into the expression. This step transforms our problem into a more numerical form: \(5(4) - 2(3)\). This substitution simplifies the expression into one that can be easily calculated, allowing for further mathematical operations.
Multiplication
Once substitution is complete, the next step is multiplication. This is where arithmetic operations with numbers replace the variables. In the expression \(5(4) - 2(3)\), we focus on multiplying the numbers associated with each part. Consider:
  • \(5 \times 4\) which equals \(20\)
  • \(2 \times 3\) which equals \(6\)
This transformation is crucial because it breaks down the problem into smaller, manageable parts. Performing these multiplications provides the concrete numerical terms that make further simplification possible.
Simplification
Simplification is the process of combining and reducing expressions to its simplest form. After completing the multiplication step and getting the terms \(20\) and \(6\), the expression \(5(4) - 2(3)\) simplifies to \(20 - 6\). Simplifying involves combining like terms and making calculations clearer and more concise. It鈥檚 a critical step that makes the final part of evaluating the expression much easier. The goal of simplification is to create an expression that is straightforward and quick to evaluate. In this case, we're nearly at our final answer.
Evaluation of Expressions
The final step in solving the expression is the evaluation. This is where the simplified expression is calculated to get a single numerical result. After applying substitution, multiplication, and simplification, the expression \(5a - 2b\) becomes a simple subtraction: \(20 - 6\). In evaluation, the focus shifts to executing this arithmetic operation. By subtracting \(6\) from \(20\), we determine the final answer: \(14\). This step is the culmination of the entire process, giving us the solution to the original expression based on the given values of \(a\) and \(b\).

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

For Exercises \(70-72,\) draw and label a figure for each relationship. (Lesson \(1-1\) ) \(\overrightarrow{F G}\) lies in plane \(M\) and contains point \(H\)

Make a conjecture based on the given information. Draw a figure to illustrate your conjecture. Lines \(\ell\) and \(m\) are perpendicular.

Construct a truth table for each compound statement. $$p \vee(\sim q \wedge r)$$

An article in a magazine states that if you get seasick, then you will get dizzy. It also says that if you get seasick, you will get an upset stomach. Suzanne says that this means that if you get dizzy, then you will get an upset stomach. Lakeisha says that she is wrong. Who is correct? Explain.

Haru made a scale model of the park near his house. Every inch represents 5 feet. If the main sidewalk in his model is 45 inches long, how long is the actual sidewalk in the park? $$\begin{aligned}&\text { F } 225 \mathrm{ft}\\\&\text { G } 125 \mathrm{ft}\\\&\begin{array}{l}\text { H } 15 \mathrm{ft} \\\\\text { J } 5 \mathrm{ft}\end{array}\end{aligned}$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

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.