/*! 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 Check whether the given number i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 71

Check whether the given number is a solution of the inequality. $$ 2 x<24 ; 8 $$

Short Answer

Expert verified
Yes, 8 is a solution to the given inequality.

Step by step solution

01

Substitute the Value

Substitute the value 8 for x in the inequality. \(2*8 < 24.\)
02

Perform the Calculation

Perform the multiplication on the left side of the inequality. \(16 < 24.\)
03

Verify the Inequality

Check if the resulting expression \(16 < 24\) is true. As 16 is indeed less than 24, this verifies that 8 is a solution to the given inequality.

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.

Solution Verification
Solution verification is an essential step in solving inequalities because it allows us to confirm whether a given number truly satisfies the inequality. This process ensures that our mathematical work is accurate and reliable.
To verify a solution, we substitute the proposed number into the inequality in place of the variable, then simplify the expression.
The result should maintain the truth of the inequality.
  • If substituting the number leads to a valid inequality (e.g., "less than" remains true), then the proposed number is indeed a solution.
  • Conversely, if the inequality becomes false or invalid, the number cannot be considered a solution.
Being diligent in solution verification helps in eliminating errors and achieving confidence in problem-solving, solidifying one's understanding of inequalities.
Mathematical Substitution
Mathematical substitution is a straightforward yet powerful tool in solving mathematical expressions including inequalities. In the context of substitution, we replace a variable with a provided number to test or evaluate an expression or inequality.
This technique is particularly useful as it allows us to simplify the problem and focus on solving it step by step.
  • For inequalities, substitution lets us see if a specific value maintains the truth of the expression.
  • Substitution helps break down complex equations into smaller, more manageable pieces.
In our example, substituting 8 for \(x\) in the inequality \(2x < 24\) converts it into \(2 \times 8 < 24\). This simple change greatly assists in subsequent calculations and solution verification.
Algebraic Expressions
Algebraic expressions form the basis of algebra, incorporating numbers, variables, and operations such as addition, subtraction, multiplication, and division. Understanding these expressions is crucial when dealing with inequalities, where expressions are compared using "less than," "greater than," and other relational signs.
An important aspect of working with algebraic expressions is being able to manipulate and simplify them without changing their fundamental relationships.
  • In inequalities, algebraic expressions help define the conditions we are examining鈥攅ither a number is a solution, or it isn鈥檛.
  • Solving inequalities involves finding the set of numbers that make the expression true, requiring a good grasp of how algebraic structures and operations interact.
Mastering algebraic expressions helps in efficiently tackling inequalities and many other branches of mathematics, paving the way to better problem-solving and critical thinking skills.

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

Write an equation of the line that passes through the points. (0,-6),(-1,7)

Write an equation in standard form of the horizontal line and the vertical line that pass through the point. $$(-3,7)$$

Use a table of values to graph the equation. Label the x-intercept and the y-intercept. $$ y=-x+8 $$

Write an equation of the line in slope-intercept form. The slope is \(\frac{1}{2} ;\) the \(y\) -intercept is \(-8\).

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. $$ -\frac{1}{2} \text { and } \frac{3}{2} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Geometry

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.