# Math Help - Help inequalities

1. ## Help inequalities

7x-5<4

4/x -4>5

2. Hello, Jerry!

The general rule for solving inequalities is something like:

. . Solve as if it were an equation except: when multiplying or
. . . . dividing by a negative quantity, reverse the inequality.

$7x - 5\:\leq \:4$

We are given: .. . $7x - 5 \;\leq \;4$

Add 5 to both sides: . $7x\;\leq\;9$

Divide by 7:. . . . . . . . $\boxed{x \;\leq \;\frac{9}{7}}$

$\frac{4}{x} -4\:\geq\:5$

There is one more rule:

. . When taking reciprocals of both sides of an inequality,
. . . . reverse the inequality.

For example: . $2 < 4\quad\Rightarrow\quad \frac{1}{2} > \frac{1}{4}$

We are given: . . . $\frac{4}{x} - 4 \;\geq \;5$

Add 4 to both sides: . $\frac{4}{x}\;\geq\;9$

Take reciprocals: . . . $\frac{x}{4} \;\leq \;\frac{1}{9}$ .
(reverse the sign)

Multiply by 4: . . . . . . $\boxed{x\;\leq\;\frac{4}{9}}$