I'm having problems solving this two. Please help
7x-5<4
4/x -4>5
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.
$\displaystyle 7x - 5\:\leq \:4$
We are given: .. . $\displaystyle 7x - 5 \;\leq \;4$
Add 5 to both sides: . $\displaystyle 7x\;\leq\;9$
Divide by 7:. . . . . . . .$\displaystyle \boxed{x \;\leq \;\frac{9}{7}}$
$\displaystyle \frac{4}{x} -4\:\geq\:5$
There is one more rule:
. . When taking reciprocals of both sides of an inequality,
. . . . reverse the inequality.
For example: .$\displaystyle 2 < 4\quad\Rightarrow\quad \frac{1}{2} > \frac{1}{4}$
We are given: . . . $\displaystyle \frac{4}{x} - 4 \;\geq \;5$
Add 4 to both sides: . $\displaystyle \frac{4}{x}\;\geq\;9$
Take reciprocals: . . . $\displaystyle \frac{x}{4} \;\leq \;\frac{1}{9}$ . (reverse the sign)
Multiply by 4: . . . . . .$\displaystyle \boxed{x\;\leq\;\frac{4}{9}}$