2010011705
Level:
A
The graph shows the set of all real numbers that satisfy the inequality
\( |2x-14| \geq 6\). Determine \( k \).
\( k = 4\)
\( k = 0\)
\( k = -4\)
\( k = 6\)
Absolute value equations and inequalities
2010011704
Level:
A
The solution set of an inequality is graphed on the number line. Determine this inequality.
\( |7-x| > 34 \)
\( |x+7| > 20 \)
\( |14-x| > 27 \)
\( |x+14| > 13 \)
2010011703
Level:
B
The solution set of the equation \( 2|45-x|-|2x-72| =0 \) is:
\( \left\{ \frac{81}2 \right\}\)
\( \emptyset\)
\( \left\{ -\frac{81}2 \right\}\)
\( \left\{ -\frac{81}2 ;\frac{81}2 \right\}\)
2010011702
Level:
A
Find the solution set of the inequality \( |15-5x| \leq 3 \).
\( \left[ \frac{12}5;\frac{18}5\right]\)
\( \left[ \frac{4}3;\frac{14}3\right]\)
\( \left[ -\frac{18}5;-\frac{12}5\right]\)
\( \left[ -\frac{14}3;-\frac{4}3\right]\)
2010011701
Level:
A
How many natural numbers belong to the solution set of the inequality \( |3x-7| < 5 \)?
\(3\)
\(4\)
\(2\)
\(1\)
2010008602
Level:
B
Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval.
\[|2x-3|+ 2|2-x |= 1-3x\]
\( \left(\frac32 ;\infty\right) \)
\( \left(-\infty;2\right) \)
\( \left(2 ;\infty\right) \)
\( \left(-\infty;\frac32\right) \)
2010008605
Level:
B
Find the sum of all the roots of the equation \( |2x+5|=|2-x| \).
\( -8\)
\( -9\)
\( -7\)
\( -1 \)
2010008604
Level:
C
Find the sum of all the roots of the given equation.
\[ \bigl|2- |x+1|\bigr|=0 \]
\( -2\)
\( 2\)
\( -4 \)
\( 0 \)
2010008603
Level:
B
Calculate for which values of the parameter \(t \in\mathbb{R} \) the given equation has no solution.
\[ |2-4x|=1-t\]
\( t\in (1 ;\infty) \)
\( t\in (-\infty;1) \)
\( t\in \left(\frac12 ;\infty\right) \)
\( t\in \left(-\infty;\frac12\right) \)
2010008601
Level:
B
Choose the equation which is, on the interval \( \left[ \frac12; 2 \right] \), equivalent to
\[ |2x-1|+2|x+5|=1-|2-x|. \]
\( (2x-1)+2(x+5)=1-(2-x) \)
\( (2x-1)+2(x+5)=1+(2-x) \)
\( (2x-1)-2(x+5)=1+(2-x) \)
\( -(2x-1)+2(x+5)=1+(2-x) \)