Question

Use the inequalities to answer the following question.

Inequality 1: 2x + 7 < -3

Inequality 2: x – 8 + 3x < -4

Which of the following values make both inequalities TRUE? Select all that apply.

A. 2/3

B. –5

C. 12

D. - 15/2

E. 325

F. –8.25

G. –10

Answer 1

verifying every options

option A 2/3

2x+7<-3

2(2/3)+7<-3

(4/3)+7<-3

4/3<-3-7

4/3<-10

4<-10×3

4<-30 (not true)

option B

-5

2x+7<-3

2(-5)+7<-3

-10+7<-3

-3<-3not true.

option C

12

2x+7<-3

2(12)+7<-3

24+7<-3

31<-3 not true

option D

-15/2

2x+7<-3

2(-15/2)+7<-3

-30/2+(7)<-3

-15+7<-3

-8<-3 true

testing for second equation

x-8+3x<-4

(-15/2)-8+3(-15/2)<-4

-7.5-8+3×-7.5<-4

-15.5-22.5<-4

-38<-4 true

option E

325

2x+7<-3

2(325)+7<-3

650+7<-3

657<-3 not true

option F

-8.25

2x+7<-3

2(-8.25)+7<-3

-16.5+7<-3

-9.5<-3 true

second equation

x-8+3x<-4

-8.25-8+3(-8.25)<-4

-16.25-24.75<-4

-41<-4 true

option G

-10

2x+7<-3

2(-10)+7<-3

-20+7<-3

-13<-3 true

x-8+3x<-4

-10-8+3(-10)<-4

-18-30<-4

-48<-4 true

answer...option D, F, G