I'm having problems solving this two. Please help

7x-5<4

4/x -4>5

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- Nov 29th 2006, 02:32 AMjerryramosHelp inequalities
I'm having problems solving this two. Please help

7x-5__<__4

4/x -4__>__5 - Nov 29th 2006, 03:53 AMSoroban
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.*

Quote:

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

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

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

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

Quote:

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

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