Question

Solve each inequality.

1. $\frac{1-7n}{5}$  > 10

Answer 1

1-7n/5 > 10

First, we can start off by making our goal to get the variable (n) on one side by itself. Let's begin by multiplying both sides by 5.
$1 - 7n \ \textgreater \ 10 \times 5$

Second, multiply 10 times 5. This can be done using a calculator, in your head, etc. (10 times 5 = 50)
$1 - 7n \ \textgreater \ 50$

Third, we will continue getting the variable alone by subtracting 1 from each side.
$-7n \ \textgreater \ 50 - 1$

Fourth, simple step. Subtract 50 - 1 (= 49).
$-7n \ \textgreater \ 49$

Fifth, now we can divide each side by -7. This will complete our goal since the variable will be by itself. Since the -(7) is carrying a negative, we can put that in front of our fraction. 
$n \ \textless \ -\frac{49}{7}$

Sixth, our last step is to simplify the fraction. We can do this by asking ourselves, what multiples by 7 to equal 49? (7 times 7 = 49), so 7 is our answer. Don't forget the negative.
$n \ \textless \ -7$

Answer: $n \ \textless \ -7$