BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

1st Edition

ISBN: 9781608408382

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 2.6, Problem 8E

To determine

To find: The solution of the inequality $|4c+5|>7$ and graph the solution if possible.

Expert Solution & Answer

Answer to Problem 8E

$(−∞,−3)∪(12,∞)$

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015, Chapter 2.6, Problem 8E , additional homework tip 1

Explanation of Solution

Given information:

The given inequality is $|4c+5|>7$ .

Concept Used:

Absolute value of a number:

The absolute value of a number ‘ $a$ ’ is equal to the distance that ‘ $a$ ’ is from zero.

$|a|={a, if a≥0, and−a, if a<0$

Rules for absolute Value inequalities:

If $|p|>a$ , $a>0$ then $p<−a$ or $u>a$ .

If $|p|<a$ , $a<0$ then $−a<p<a$ .

If $|p|≥a$ , $a>0$ then $p≤−a$ or $p≥a$ .

If $|p|≤a$ , $a>0$ then $−a≤p≤a$ .

Calculation:

Use the rule of absolute inequalities: If $|p|>a$ , $a>0$ then $p<−a$ or $u>a$ .

Case 1:

$4c+5<−7$

Subtract $5$ from both the sides.

$4c+5−5<−7−54c<−12$

Divide by $4$ on both the sides.

$4c4<−124c<−3$

Case 2:

$4c+5>7$

Subtract $5$ from both the sides.

$4c+5−5>7−54c>2$

Divide by $4$ on both the sides.

$4c4>24c>12$

Graph:

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015, Chapter 2.6, Problem 8E , additional homework tip 2

From the above graph, it is observed that $x$ represents all real number that are less than $−3$ or greater than $12$ .

Therefore, the solution of the given inequality is $(−∞,−3)∪(12,∞)$ .

Chapter 2.6, Problem 7E

Chapter 2.6, Problem 9E

Chapter 2 Solutions

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - Prob. 51E Ch. 2.1 - Prob. 52E Ch. 2.1 - Prob. 53E Ch. 2.1 - Prob. 54E Ch. 2.1 - Prob. 55E Ch. 2.1 - Prob. 56E Ch. 2.1 - Prob. 57E Ch. 2.1 - Prob. 58E Ch. 2.1 - Prob. 59E Ch. 2.1 - Prob. 60E Ch. 2.1 - 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The solution of the inequality | 4 c + 5 | &gt; 7 and graph the solution if possible.

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To find: The solution of the inequality |4c+5|>7<m:math><m:mrow><m:mrow><m:mo>|</m:mo><m:mrow><m:mn>4</m:mn><m:mi>c</m:mi><m:mo>+</m:mo><m:mn>5</m:mn></m:mrow><m:mo>|</m:mo></m:mrow><m:mo>&gt;</m:mo><m:mn>7</m:mn></m:mrow></m:math> and graph the solution if possible.

Answer to Problem 8E

Explanation of Solution

Chapter 2 Solutions

The solution of the inequality | 4 c + 5 | > 7 and graph the solution if possible.

To find: The solution of the inequality $|4c+5|>7$ and graph the solution if possible.