Question

20 PTS!!! HELP PLZ!!!

Solve each inequality.


1. d + 7 > 7d + 3 over 3

2. a - 6 over 3 > a + 2

3. d over 2 < 3d over 2 + 6


4.Write and solve an inequality for the problem.

Twice a number, n, subtracted from 36 is less than 15 more than one third the number. Find all possible values for the number.

Answer 1

`1.\\d+7>(7d+3)/(3)\qquad\text{multiply both sides by 3}\\\\3d+21>7d+3\qquad\text{subtract 21 from both sides}\\\\3d>7d-18\qquad\text{subtract 7d from both sides}\\\\-4d>-18\qquad\text{change the signs}\\\\4d<18\qquad\text{divide both sides by 4}\\\\\boxed{d<4.5}`

`2.\\(a-6)/(3)>a+2\qquad\text{multiply both sides by 3}\\\\a-6>3a+6\qquad\text{add 6 to both sides}\\\\a>3a+12\qquad\text{subtract 3a from both sides}\\\\-2a>12\qquad\text{change the signs}\\\\2a<-12\qquad\text{divide both sides by 2}\\\\\boxed{a<-6}`

`3.\\(d)/(2)<(3d)/(2)+6\qquad\text{multiply both sides by 2}\\\\d<3d+12\qquad\text{subtract 3d from both sides}\\\\-2d<12\qquad\text{change the signs}\\\\2d>-12\qquad\text{divide both sides by 2}\\\\\boxed{d>-6}`

`4.\\36-2n<(1)/(3)n+15\qquad\text{subtract 36 from both sides}\\\\-2n<(1)/(3)n-21\qquad\text{multiply both sides by 3}\\\\-6n<n-63\qquad\text{subtract n from both sides}\\\\-7n<-63\qquad\text{change the signs}\\\\7n>63\qquad\text{divide both sides by 7}\\\\\boxed{n>9}`