Answer The solution set is { d | d > − 105 } Explanation Given: The inequality equation: 2 − d 5 < 23 Concept Used: In mathematics , an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b. There are four different types of inequalities: Greater than − ( > ) ; Less than − ( < ) ; Greater than or equal to − ( ≥ ) ; Less than or equal to − ( ≤ ) For Inequality equation: If b > c ⇒ c < b or b < c ⇒ c > b Rules for solving inequality equations: These things do not affect the direction of the inequality: Add (or subtract) a number from both sides Multiply (or divide) both sides by a positive number Simplify a side But these things do change the direction of the inequality (" < " becomes " > "for example): Multiply (or divide) both sides by a negative number Swapping left and right hand sides Calculation: The inequality equation: 2 − d 5 < 23 Solve: 2 − d 5 < 23 2 − 2 − d 5 < 23 − 2 [ Subtract 2 from both sides ] − d 5 < 21 − 5 · − d 5 > − 5 · 21 [ Multiply both sides by − 5 and reverse the inequality ] d > − 105 Solution set: ( − 105 , ∞ ) or { d | d > − 105 } Check the solution set when d = 0 2 − d 5 < 23 2 − 0 5 < 23 2 − 0 < 23 2 < 23 [ True statement ] Solution set on the number line An open circle is used for greater than (>) or less than (<). The point is not part of the solution. The graph then extends endlessly in one direction. Solution of the inequality equation is ( − 105 , ∞ ) or { d | d > − 105 } Thus, the solution of the inequality equation is { d | d > − 105 }

1st Edition

ISBN: 9780078884801

Author: McGraw-Hill/Glencoe

Publisher: Glencoe/McGraw-Hill School Pub Co

See similar textbooks

Videos

Question

Chapter 9.3, Problem 56SR

To determine

Solve for the unknown variable from the inequality equation.

Expert Solution & Answer

Answer to Problem 56SR

The solution set is ${ d | d>−105 }$

Explanation of Solution

Given:

The inequality equation: $2−d5<23$

Concept Used:

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b.

There are four different types of inequalities:

Greater than − $(>)$ ; Less than − $(<)$ ; Greater than or equal to − $(≥)$ ; Less than or equal to − $(≤)$

For Inequality equation: If $b>c ⇒ c < b or b < c ⇒ c > b$

Rules for solving inequality equations:

These things do not affect the direction of the inequality:

Add (or subtract) a number from both sides
Multiply (or divide) both sides by a positive number
Simplify a side

But these things do change the direction of the inequality (" $<$ " becomes " $>$ "for example):

Multiply (or divide) both sides by a negative number
Swapping left and right hand sides

Calculation:

The inequality equation: $2−d5<23$

Solve:

$2−d5<232−2−d5<23−2 [ Subtract 2 from both sides ] −d5<21−5 · −d5> −5 · 21 [Multiply both sides by −5 and reverse the inequality ] d > −105$

Solution set: $( −105 , ∞ ) or { d | d>−105 }$

$Check the solution set when d = 02−d5<232−05<232−0<232<23 [ True statement ]$

Solution set on the number line

An open circle is used for greater than (>) or less than (<). The point is not part of the solution. The graph then extends endlessly in one direction.

Algebra 1, Chapter 9.3, Problem 56SR

Solution of the inequality equation is $( −105 , ∞ ) or { d | d>−105 }$

Thus, the solution of the inequality equation is ${ d | d>−105 }$

Chapter 9.3, Problem 55SR

Chapter 9.3, Problem 57S

Chapter 9 Solutions

Algebra 1

Ch. 9.1 - Prob. 67PPS Ch. 9.1 - Prob. 68HP Ch. 9.1 - Prob. 69HP Ch. 9.1 - Prob. 70HP Ch. 9.1 - Prob. 71HP Ch. 9.1 - Prob. 72HP Ch. 9.1 - Prob. 73HP Ch. 9.1 - Prob. 74HP Ch. 9.1 - Prob. 75STP Ch. 9.1 - Prob. 76STP

Additional Math Textbook Solutions

Find more solutions based on key concepts

Women’s Heights Suppose college women’s heights are approximately Normally distributed with a mean of 65 inches...

Introductory Statistics

In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 43. f( x )=x+| x |

Precalculus

Find how many SDs above the mean price would be predicted to cost.

Intro Stats, Books a la Carte Edition (5th Edition)

Identifying Binomial Distributions. In Exercises 5–12, determine whether the given procedure results in a binom...

Elementary Statistics (13th Edition)

In track, the second lane from the inside of the track is longer than the inside lane. Use this information to ...

A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

The following set of data is from sample of n=5: a. Compute the mean, median, and mode. b. Compute the range, v...

Basic Business Statistics, Student Value Edition

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.