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

[tex]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}\\\\\dfrac{3d}{3}<-\dfrac{3}{3}\\\\d<-1\\\\-------------------------\\\text{We have}\ d<5\ \text{or}\ d<-1.\ \text{Therefore}\ d<5.[/tex]

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Amphitrite1040 Amphitrite1040 · Answer 2 · 2019-04-14T19:14:35+02:00

[tex]\bf{Hey\ there!}[/tex]

[tex]\bf{For:\ 4d<5+3d}[/tex]

[tex]\bf{\underline{REVERSE}\ the\ equation:4d<3d+5}[/tex]

[tex]\bf{First\ the\ term\ 3d\ on\ each\ of\ your\ sides!\downarrow}[/tex]

[tex]\boxed{\boxed{\bf{Thus\ the\ answer\ is:d<5}}}\checkmark[/tex]

[tex]\bf{For:8-3d>11}[/tex]

[tex]\bf{\underline{REVERSE}\ the\ equation:-3d+8>11}[/tex]

[tex]\bold{First\ you\ have\ to\ subtract\ by\ 8\ on\ your\ sides!\downarrow}[/tex]

[tex]\bf{-3d+8-8>11-8}[/tex]

[tex]\bf{Cancel:8-8\ because\ 8-8\ equals\ 0}[/tex]

[tex]\bf{Keep:11-8\ because\ that\ helps\ us\ solve\ for\ our\ answer}[/tex]

[tex]\bf{11-8=3}[/tex]

[tex]\bf{New\ problem:-3d>3}[/tex]

[tex]\bf{Divide\ each\ of\ your\ sides\ by\ -3}[/tex]

[tex]\bf{\frac{-3d}{-3}>\frac{3}{-3}}[/tex]

[tex]\bf{Cancel\ out:\frac{-3d}{-3}\ because\ it\ equals\ 1}[/tex]

[tex]\bf{Keep:\frac{3}{-3}\ because\ it\ helps\ us\ solve\ for\ your\ answer}[/tex]

[tex]\bf{\frac{3}{-3}=-1}[/tex]

[tex]\boxed{\boxed{\bf{Thus\ your\ answer\ is:d<-1}}}\checkmark[/tex]

[tex]\bf{Good\ luck\ on\ your\ assignment\ and\ enjoy\ your\ day!}[/tex]

[tex]\frak{LoveYourselfFirst:)}[/tex]