/*! 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 44 Find the value of each of the fo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 44

Find the value of each of the following expressions when \(x=-3\). $$4 x+7$$

Short Answer

Expert verified
The expression evaluates to \(-5\) when \(x=-3\).

Step by step solution

01

Substitute the Value of x

First, we need to substitute the given value of \(x\) into the expression. The expression given is \(4x + 7\), and we are asked to evaluate it when \(x = -3\). So, substitute \(-3\) for \(x\) in the expression, which becomes \(4(-3) + 7\).
02

Calculate the Multiplication

Now, calculate the multiplication operation. Multiply 4 by \(-3\), resulting in \(-12\). So, the expression becomes \(-12 + 7\).
03

Perform the Addition

Finally, perform the addition operation. Add \(-12\) and 7, which gives \(-5\). So, the value of the expression when \(x=-3\) is \(-5\).

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 an expression involves finding its value by substituting variables with specific numbers. In the given exercise, you are asked to evaluate the expression \(4x + 7\) when \(x = -3\). This process can often be broken down into a few straightforward steps:
  • Start by substituting the value of the variable into the expression.
  • Next, follow the order of operations (often remembered by PEMDAS/BODMAS) to simplify the expression. This often involves performing multiplication or division before addition or subtraction.

In our example, we substitute \(-3\) for \(x\), and then simplify the expression step by step, leading to the result of \(-5\). Making sure to work through each calculation carefully ensures that you get the correct result.
Integer Arithmetic
Integer arithmetic involves conducting mathematical operations with whole numbers, including positive numbers, negative numbers, and zero. This type of arithmetic is foundational in prealgebra and is crucial when evaluating algebraic expressions.
  • Multiplication and Division: When multiplying or dividing integers, the sign of the result depends on the signs of the numbers involved. For instance:
    • Multiplying two positive or two negative numbers gives a positive result.
    • Multiplying a positive number by a negative number yields a negative result.
  • Addition and Subtraction: When adding or subtracting integers, consider the signs again. Adding a negative number is the same as subtracting its positive counterpart.

In our expression, multiplying \(4\) with \(-3\) results in \(-12\). Following that, adding \(-12\) and \(7\) gives the result of \(-5\). Careful attention to the signs helps avoid common mistakes.
Prealgebra
Prealgebra is an essential mathematical stepping stone. It prepares you for more advanced algebra by focusing on core concepts like variables and arithmetic operations. Understanding prealgebra involves:
  • Grasping basic arithmetic operations including addition, subtraction, multiplication, and division.
  • Familiarity with working with variables, where letters like 'x' can represent numbers.
  • Learning how to evaluate expressions by substituting variables with given numbers.

In your exercise, using prealgebra concepts enabled the evaluation of \(4x + 7\) by understanding how to substitute \(x\) with \(-3\). This type of practice is crucial for gaining confidence and skill in solving algebraic equations. Mastering prealgebra provides a solid foundation for tackling more complex mathematical problems in the future.

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

Expand and multiply. $$(4 x+5)^{2}$$

Multiply the following expressions. $$(2 x-5)(3 x-4)$$

Multiply the following expressions. $$\left(x^{4}+x^{2}\right) x^{3}$$

Complete the following table. $$\begin{array}{|c|}\hline \text { Number } & \text { Square } \\\\\hline x & x^2 \\\\\hline-2.5 & \\\\\hline-1.5 & \\\\\hline-0.5 & \\\\\hline 0 & \\\\\hline 0.5 & \\\\\hline 1.5 & \\\\\hline 2.5 & \\\\\hline\end{array}$$

Expand and multiply. $$(x+4)^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

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.