Solution assignment 08 Inequalities with fractions

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Assignment 8

Solve:

$\displaystyle\frac{2x}{x+2}>3$

Solution

The best way to solve such an inequality is to make the right-hand side equal to $0$ $0$ So we take $3$ to the left-hand side and convert the fractions to the same denominator.

$\displaystyle\frac{2x}{x+2}-3\displaystyle\frac{x+2}{x+2}>0$

$\displaystyle\frac{2x-3x-6}{x+2}>0$

$\displaystyle\frac{x+6}{x+2}<0$

For both the numerator and the denominator we draw number lines, as well as for the quotient.

$x+6$ ---------------(-6)++++++++++++++
$x+2$ --------------------------------(-2)+++++
quotient +++++++(-6)------------(-2)+++++

The third line shows that the inequality is satisfied if:

$-6<x<-2$

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Solution assignment 08 Inequalities with fractions

Assignment 8

Solution

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