Question

Solve each inequality. 1. ac{1-7n}{5} " alt=" \frac{1-7n}{5} " align="absmiddle" class="latex-formula">  > 10

Answer 1

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

$\frac{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.

$\frac{-7n}{7}$$>\frac{49}{-7}$

$n$

The solution to the inequality is n<-7.

Answer 2

$Solution, \frac{1-7n}{5}>10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x$

$Steps:$

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

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

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

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

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

$\mathrm{Simplify}, 7n$

$\mathrm{Divide\:both\:sides\:by\:}7, \frac{7n}{7}$

$\mathrm{Simplify}, n$

The correct answer is n<-7

Hope This Helps!!!