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Exercises: Linear functions as lines in coordinate systems

Determine for which x-values of $f (x) > 0$ .

$f (x) = 0.4 x + 1$

For this task you need the following basic knowledge: solve inequalities
$f (x)$ $>$ $0$
↓
Insert the function term.
$0.4 x + 1$ $>$ $0$ $- 1$
↓
Sort by x-terms and numbers.
$0.4 x$ $>$ $- 1$ $: 0.4$
↓
Solve for x (observe $0.4 > 0$ , the inequality sign remains).
$x$ $>$ $- \frac{1}{0.4} = - 2.5$
$ f (x)$ is greater than zero for all $x > - 2.5$ .

$f (x) = - 1.5 (x - 2)$

$f (x) = \frac{x}{5} - \frac{7}{5}$

For this task you need the following basic knowledge: solve inequalities.
$f (x)$ $>$ $0$
↓
Insert functional equation.
$\frac{x}{5} - \frac{7}{5}$ $>$ $0$ $+ \frac{7}{5}$
↓
Sort by x-terms and numbers.
$\frac{x}{5}$ $>$ $\frac{7}{5}$ $\cdot 5$
↓
Solve for x (5>0, so no change to the inequality sign)
$x$ $>$ $7$
For $x > 7$ is $f (x)$ positive.

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