Question

Show work
only do those
32,34,36,38,40

Answer 1

Answer: see below

Explanation:

`32)\quad (3)/(5)(x-12)>x-24`

3(x - 12) > 5(x - 24)

3x - 36 > 5x - 120

-5x -5x

-2x - 36 > -120

+36 +36

-2x > -84

÷ -2 ↓ ÷ -2

x < 42

Graph: ←------------o

42

34) 6[5y - (3y - 1)] ≥ 4(3y - 7)

6[5y - 3y + 1] ≥ 4(3y - 7)

6{2y + 1] ≥ 4(3y - 7)

12y + 6 ≥ 12y - 28

-12y -12y

6 ≥ -28

TRUE so the solution is All Real Numbers

Graph: ←-----------------------→

36) BC + AC > AB

4 + 8 - AB > AB

12 - AB > AB

+AB +AB

12 > 2AB

÷2 ÷2

6 > AB

AB < 6

`38)\quad (1)/(2)(y-16)\geq y+2\quad ;\text{claim}\ y\leq 20`

Check: let y = 16

then
`(1)/(2)`(16 - 16) ≥ 16 + 2

0 ≥ 18

FALSE so the claim is wrong

40) question not provided in the image so I cannot give a solution.