Answer The graph of the given inequality is Explanation Given: The inequality 5 x − 2 y ≤ 6 Concept Used: The graph of a linear inequality in two variables shows all the solutions of the inequality in a coordinate plane. Calculation: Given the inequality 5 x − 2 y ≤ 6 Consider the corresponding equation 5 x − 2 y = 6 Graphing the equation 5 x − 2 y = 6 For x = 0 5 x − 2 y = 6 5 ( 0 ) − 2 y = 6 Substitute x = 0 0 − 2 y = 6 − 2 y − 2 = 6 − 2 Divide both sides by − 2 y = − 3 For y = 0 5 x − 2 y = 6 5 x − 2 ( 0 ) = 6 Substitute y = 0 5 x = 6 5 x 5 = 6 5 Divide both sides by 5 x = 6 5 The points on the equation 5 x − 2 y = 6 are x 0 6 5 y − 3 0 Since, in the given inequality 5 x − 2 y ≤ 6 , the symbol is ≤ So, plotting the graph of the equation 5 x − 2 y = 6 using a solid line. We have, Testing a point on either side of the solid line Consider a coordinate ( 0 , 0 ) on left side of the solid line. Substituting the coordinate ( 0 , 0 ) in the given inequality on both sides, we have 5 x − 2 y ≤ 6 5 ( 0 ) − 2 ( 0 ) ≤ 6 Substitute ( 0 , 0 ) 0 ≤ 6 Which is True Thus, ( 0 , 0 ) is the solution of the given inequality. Shading the half-plane that contains ( 0 , 0 ) . The graph of the given inequality is Conclusion: The graph of the given inequality is

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN: 9781680331141

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 5.6, Problem 29E

To determine

ToGraph:The inequality 5x−2y≤6 in a coordinate plane.

Expert Solution & Answer

Answer to Problem 29E

The graph of the given inequality is

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015, Chapter 5.6, Problem 29E , additional homework tip 1

Explanation of Solution

Given:

The inequality 5x−2y≤6

Concept Used:

The graph of a linear inequality in two variables shows all the solutions of the inequality in a coordinate plane.

Calculation:

Given the inequality 5x−2y≤6

Consider the corresponding equation 5x−2y=6

Graphing the equation 5x−2y=6

For x=0

5x−2y=65(0)−2y=6 Substitute x=00−2y=6−2y−2=6−2Divide both sides by −2

y=−3

For y=0

5x−2y=65x−2(0)=6 Substitute y=05x=65x5=65 Divide both sides by 5

x=65

The points on the equation 5x−2y=6 are

x	0	65
y	−3	0

Since, in the given inequality 5x−2y≤6 , the symbol is ≤

So, plotting the graph of the equation 5x−2y=6 using a solid line. We have,

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015, Chapter 5.6, Problem 29E , additional homework tip 2

Testing a point on either side of the solid line

Consider a coordinate (0,0) on left side of the solid line.

Substituting the coordinate (0,0) in the given inequality on both sides, we have

5x−2y≤65(0)−2(0)≤6 Substitute (0,0)0≤6 Which is True

Thus, (0,0) is the solution of the given inequality.

Shading the half-plane that contains (0,0) . The graph of the given inequality is

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015, Chapter 5.6, Problem 29E , additional homework tip 3

Conclusion:

The graph of the given inequality is

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015, Chapter 5.6, Problem 29E , additional homework tip 4

Chapter 5.6, Problem 28E

Chapter 5.6, Problem 30E

Chapter 5 Solutions

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - 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Prob. 49E Ch. 5.7 - Prob. 50E Ch. 5.7 - Prob. 51E Ch. 5.7 - Prob. 52E Ch. 5.7 - Prob. 53E Ch. 5.7 - Prob. 54E Ch. 5.7 - Prob. 55E Ch. 5 - Prob. 1CR Ch. 5 - Prob. 2CR Ch. 5 - Prob. 3CR Ch. 5 - Prob. 4CR Ch. 5 - Prob. 5CR Ch. 5 - Prob. 6CR Ch. 5 - Prob. 7CR Ch. 5 - Prob. 8CR Ch. 5 - Prob. 9CR Ch. 5 - Prob. 10CR Ch. 5 - Prob. 11CR Ch. 5 - Prob. 12CR Ch. 5 - Prob. 13CR Ch. 5 - Prob. 14CR Ch. 5 - Prob. 15CR Ch. 5 - Prob. 16CR Ch. 5 - Prob. 17CR Ch. 5 - Prob. 18CR Ch. 5 - Prob. 19CR Ch. 5 - Prob. 20CR Ch. 5 - Prob. 21CR Ch. 5 - Prob. 22CR Ch. 5 - Prob. 1CT Ch. 5 - Prob. 2CT Ch. 5 - Prob. 3CT Ch. 5 - Prob. 4CT Ch. 5 - Prob. 5CT Ch. 5 - Prob. 6CT Ch. 5 - Prob. 7CT Ch. 5 - Prob. 8CT Ch. 5 - Prob. 9CT Ch. 5 - Prob. 10CT Ch. 5 - Prob. 11CT Ch. 5 - Prob. 12CT Ch. 5 - Prob. 13CT Ch. 5 - Prob. 14CT Ch. 5 - Prob. 15CT Ch. 5 - Prob. 1CA Ch. 5 - Prob. 2CA Ch. 5 - Prob. 3CA Ch. 5 - Prob. 4CA Ch. 5 - Prob. 5CA Ch. 5 - Prob. 6CA Ch. 5 - Prob. 7CA Ch. 5 - Prob. 8CA Ch. 5 - Prob. 9CA Ch. 5 - Prob. 10CA

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ToGraph: The inequality 5 x − 2 y ≤ 6 in a coordinate plane.

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ToGraph:The inequality 5x−2y≤6 in a coordinate plane.

Answer to Problem 29E

Explanation of Solution

Chapter 5 Solutions