Question

Solve each inequality.

1.
`(1-7n)/(5)`  > 10

Answer 1

`Solution, (1-7n)/(5)>10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-7\right)\end{bmatrix}`

`Steps:`

`\mathrm{Multiply\:both\:sides\:by\:}5, (5\left(1-7n\right))/(5)>10\cdot \:5`

`\mathrm{Simplify}, 1-7n>50`

`\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}, 1-7n-1>50-1`

`\mathrm{Simplify}, -7n>49`

`Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right), \left(-7n\right)\left(-1\right)<49\left(-1\right)`

`\mathrm{Simplify}, 7n<-49`

`\mathrm{Divide\:both\:sides\:by\:}7, (7n)/(7)<(-49)/(7)`

`\mathrm{Simplify}, n<-7`

The correct answer is n<-7

Hope This Helps!!!

Answer 2

First multiply 5 on both sides to get rid of the five on the bottom.

`(1-7n)/(5*5)`
`>10*5`

`1-7n>50`

Subtract 1 from both sides of the inequality.

`1-1-7n>50-1`

`-7n>49`

Divide -7 on both sides, and flip the inequality sign since we are dividing by a negative.

`(-7n)/(7)`
`>(49)/(-7)`

`n<-7`

The solution to the inequality is n<-7.