Answer False Explanation Given: The Inequality: 120 d > 40 ; d = 3 Concept Used: 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 If there is a parenthesis ( ) on the interval, then we use the strict inequality symbols < or > If there is a bracket [ ] on the interval, then we use the inequality symbols Calculation: 120 d > 40 d · 120 d > d · 40 [ Multiply d both sides by ] 120 > 40 d 40 d < 120 [ b > c ⇒ c < b ] 40 d 40 < 120 40 d < 3 Solution d < 3 means the number less than 3, this means 3 is not included. Solution d = 3 is not a true solution. Thus, it means d = 3 is not true. False

Glencoe Math Accelerated, Student Edition

1st Edition

ISBN: 9780076637980

Author: McGraw-Hill Glencoe

Publisher: MCG

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Question

Chapter 8.6, Problem 22IP

To determine

Find for the given value, state whether the inequality $120d>40 ; d=3$ is true or false.

Expert Solution & Answer

Answer to Problem 22IP

False

Explanation of Solution

Given:

The Inequality: $120d>40 ; d=3$

Concept Used:

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
If there is a parenthesis $()$ on the interval, then we use the strict inequality symbols $< or>$

If there is a bracket $[]$ on the interval, then we use the inequality symbols

Calculation:

$120d>40d · 120d>d · 40 [ Multiply d both sides by ] 120>40d40d<120 [ b>c ⇒ c<b ]40d40< 12040d<3$

Solution $d<3$ means the number less than 3, this means 3 is not included.

Solution d = 3 is not a true solution.

Glencoe Math Accelerated, Student Edition, Chapter 8.6, Problem 22IP

Thus, it means d = 3 is not true. False

Chapter 8.6, Problem 21IP

Chapter 8.6, Problem 23IP

Chapter 8 Solutions

Glencoe Math Accelerated, Student Edition

Ch. 8.1 - Prob. 1GP Ch. 8.1 - Prob. 2GP Ch. 8.1 - Prob. 3GP Ch. 8.1 - Prob. 4GP Ch. 8.1 - Prob. 5GP Ch. 8.1 - Prob. 6GP Ch. 8.1 - Prob. 7GP Ch. 8.1 - Prob. 8GP Ch. 8.1 - Prob. 9GP Ch. 8.1 - Prob. 10GP

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Find for the given value, state whether the inequality 120 d &gt; 40 ; d = 3 is true or false .

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Answer to Problem 22IP

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Chapter 8 Solutions

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Find for the given value, state whether the inequality 120 d > 40 ; d = 3 is true or false .