#### Chapter 3 Inequalities in one Variable

Section 3.4 Final Test

# 3.4.1 Final Test Module 3

This is a test for submission:
• Unlike open exercises, no hints for formulating mathematical expressions are provided.
• The test can be restarted or interrupted at any time.
• The test can be terminated and submitted using the buttons at the end of the page, or reset.
• The test can be attempted several times. Only the last version will be included in the statistics.

##### Exercise 3.4.1
Find the value of the parameter $\alpha$ such that the inequality $2{x}^{2}\le x-\alpha$ has exactly one solution:
1. The parameter value is $\alpha$$=$ .
2. In this case $x$$=$
is the only solution of the inequality.

##### Exercise 3.4.2
Find an absolute value function $g\left(x\right)$ describing the following graph as easy as possible.

Graph of the function $g\left(x\right)$.
Try to find a representation of the form $g\left(x\right)=|x+a|+bx+c$. The kink in the graph indicates how the absolute value term looks like.
1. Find the solution set of the inequality $g\left(x\right)\le x$ by means of the graph.
The solution set is $L$$=$ .
2. $g\left(x\right)$$=$
.
Absolute values can be entered in the form betrag(x-a) or abs(x-a).

##### Exercise 3.4.3
Which positive real numbers $x$ satisfy the following inequalities?
1. $|3x-6|\le x+2$ has the solution set $L$$=$
(written as an interval).
2. $\frac{x+1}{x-1}\ge 2$ has the solution set $L$$=$
(written as an interval).
Enter open intervals in the form $\left(3;5\right)$, closed intervals in the form $\left[3;5\right]$. Infinity can be entered a a word or shortly a infty. Do not use notation $\right]a;b\left[$ for open intervals. Sets can be entered by listing the elements $\left\{1;2;3\right\}$. For the set brackets enter AltGr+7 or AltGr+0, respectively.

The test evaluation will be displayed here!