Question

What is the inequality 4d<5+3d or 8-3d >11

Answer 1

`\bf{Hey\ there!}`

`\bf{For:\ 4d<5+3d}`

`\bf{\underline{REVERSE}\ the\ equation:4d<3d+5}`

`\bf{First\ the\ term\ 3d\ on\ each\ of\ your\ sides!\downarrow}`

`\boxed{\boxed{\bf{Thus\ the\ answer\ is:d<5}}}\checkmark`

`\bf{For:8-3d>11}`

`\bf{\underline{REVERSE}\ the\ equation:-3d+8>11}`

`\bold{First\ you\ have\ to\ subtract\ by\ 8\ on\ your\ sides!\downarrow}`

`\bf{-3d+8-8>11-8}`

`\bf{Cancel:8-8\ because\ 8-8\ equals\ 0}`

`\bf{Keep:11-8\ because\ that\ helps\ us\ solve\ for\ our\ answer}`

`\bf{11-8=3}`

`\bf{New\ problem:-3d>3}`

`\bf{Divide\ each\ of\ your\ sides\ by\ -3}`

`\bf{(-3d)/(-3)>(3)/(-3)}`

`\bf{Cancel\ out:(-3d)/(-3)\ because\ it\ equals\ 1}`

`\bf{Keep:(3)/(-3)\ because\ it\ helps\ us\ solve\ for\ your\ answer}`

`\bf{(3)/(-3)=-1}`

`\boxed{\boxed{\bf{Thus\ your\ answer\ is:d<-1}}}\checkmark`

`\bf{Good\ luck\ on\ your\ assignment\ and\ enjoy\ your\ day!}`

`\frak{LoveYourselfFirst:)}`

Answer 2

d < 5

Explanation:

`4d<5+3d\qquad\text{subtract 3d from both sides}\\\\4d-3d<5+3d-3d\\\\d<5\\--------------------------\\8-3d>11\qquad\text{subtract 8 from both sides}\\\\8-8-3d>11-8\\\\-3d>3\qquad\text{change the signs}\\\\3d<-3\qquad\text{divide both sides by 3}\\\\(3d)/(3)<-(3)/(3)\\\\d<-1\\\\-------------------------\\\text{We have}\ d<5\ \text{or}\ d<-1.\ \text{Therefore}\ d<5.`