Solution assignment 07 Inequalities with fractions

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Asignment 7

Solve:

$\displaystyle\frac{3}{x}<1$

Solution

The best way to solve such an inequality is to make the right-hand side equal to $0$ . So we take $1$ to the left-hand side and convert the fractions to the same denominator.

$\displaystyle\frac{3}{x}-1<0$

$\displaystyle\frac{3}{x}-\displaystyle\frac{x}{x}<0$

$\displaystyle\frac{3-x}{x}<0$

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

For both numerator and denominator we draw a number line, as well as for the quotient:

$x-3$ --------------------(3)++++++
$x$ --------------(0)++++++++++++++
quotient ++++(0)--------(3)++++++

The third line shows that the values of $x$ that satisfy the inequality are:

$x<0$ or $x>3$

Return to Assignments Inequalities with fractions

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Solution assignment 07 Inequalities with fractions

Asignment 7

Solution

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