# How do you solve (x+12)/x<7?

May 9, 2015

Solve $\frac{x + 12}{x} < 7$ .

$\left(\frac{\cancel{x}}{\cancel{x}}\right) + \frac{12}{x} < 7$

$1 + \frac{12}{x} < 7$

Subtract $1$ from both sides.

$\frac{12}{x} < 7 - 1$

$\frac{12}{x} < 6$

Multiply both sides by $x$.

$\frac{12}{\cancel{x}} \cdot \cancel{x} < 6 \cdot x$ =

$12 < 6 x$

Divide both sides by $6$.

$\frac{12}{6} < \cancel{6} \frac{x}{\cancel{6}}$

$2 < x$

Flip to get $x$ on the left side.(optional)

$x > 2$.