1003187309
Level:
B
Give the number which satisfies the equation \( |6x+4|+4x=0 \).
\( x=-2 \)
\( x=1 \)
\( x=2 \)
\( x=-1 \)
Absolute value equations and inequalities
1003187402
Level:
B
For a given parameter \( a\in\mathbb{R} \) the number \( \pi-\sqrt[3]5-\sqrt2+7 \) represents one of the solutions of the equation \( |2x|=2a^2 \). Which of the following numbers is also the solution of this equation?
\( \sqrt2-7+\sqrt[3]5-\pi \)
\( \sqrt{7-\pi+\sqrt[3]5+\sqrt2} \)
\( \sqrt[3]5-\pi-\sqrt2-7 \)
\( \sqrt{\pi-\sqrt[3]5-\sqrt2+7} \)
1003187411
Level:
B
The solution set of the equation \( 3|51-x|-2|x-81| =0 \) is:
\( \{-9;63\} \)
\( \{63\} \)
\( \{9;63\} \)
\( \{-63;-9\} \)
2010008501
Level:
B
Find all \( t\in\mathbb{R} \), such that the following equation with the variable \( x \) has exactly two solutions.
\[ |x+2|+3=t-1 \]
\( t\in(4;\infty) \)
\( t\in(-2;\infty) \)
\( t\in\{4\} \)
\( \mathbb{R}\)
2010008504
Level:
B
Give the number which satisfies the equation \( |x+2|-1=x+3\).
\(-3\)
\( -2 \)
\( 0 \)
\( 1 \)
2010008601
Level:
B
Choose the equation which is, on the interval \( \left[ \frac12; 2 \right] \), equivalent to
\[ |2x-1|+2|x+5|=1-|2-x|. \]
\( (2x-1)+2(x+5)=1-(2-x) \)
\( (2x-1)+2(x+5)=1+(2-x) \)
\( (2x-1)-2(x+5)=1+(2-x) \)
\( -(2x-1)+2(x+5)=1+(2-x) \)
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.
\[|2x-3|+ 2|2-x |= 1-3x\]
\( \left(\frac32 ;\infty\right) \)
\( \left(-\infty;2\right) \)
\( \left(2 ;\infty\right) \)
\( \left(-\infty;\frac32\right) \)
2010008603
Level:
B
Calculate for which values of the parameter \(t \in\mathbb{R} \) the given equation has no solution.
\[ |2-4x|=1-t\]
\( t\in (1 ;\infty) \)
\( t\in (-\infty;1) \)
\( t\in \left(\frac12 ;\infty\right) \)
\( t\in \left(-\infty;\frac12\right) \)
2010008605
Level:
B
Find the sum of all the roots of the equation \( |2x+5|=|2-x| \).
\( -8\)
\( -9\)
\( -7\)
\( -1 \)
2010011703
Level:
B
The solution set of the equation \( 2|45-x|-|2x-72| =0 \) is:
\( \left\{ \frac{81}2 \right\}\)
\( \emptyset\)
\( \left\{ -\frac{81}2 \right\}\)
\( \left\{ -\frac{81}2 ;\frac{81}2 \right\}\)