1003187301
Level:
A
Which equation has the solutions \( -1 \) and \( 9 \)?
\( |2x-8|=10 \)
\( |2x-10|=8 \)
\( |2x+8|=10 \)
\( |2x+10|=8 \)
Absolute value equations and inequalities
1003187411
Level:
B
The solution set of the equation \( 3|51-x|-2|x-81| =0 \) is:
\( \{-9;63\} \)
\( \{63\} \)
\( \{9;63\} \)
\( \{-63;-9\} \)
1003187410
Level:
C
How many integers are in the solution set of the given inequalities?
\[ \left|\sqrt{17}-2x\right| \leq 5 \text{ and } \left|2x-\sqrt{17}\right| \leq 5 \]
\( 5 \)
\( 4 \)
\( 6 \)
\( 7 \)
1103187409
Level:
A
The graph shows the set of all real numbers that satisfy the inequality
\( |3x-12| \leq 15 \). Determine \( k \).
\( k = 9 \)
\( k = 4 \)
\( k = 5 \)
\( k = 2 \)
1103187408
Level:
A
Identify the graph which shows the solution set of the inequality \( |2x-12| > 6 \).
1003187407
Level:
A
Find the solution set of the inequality \( |12-6x| < 2 \).
\( \left( \frac53;\frac73 \right) \)
\( \left( -\frac73;-\frac53 \right) \)
\( \left( -\frac73;\frac53 \right) \)
\( \left( -\frac53;\frac73 \right) \)
1003187406
Level:
A
How many natural numbers belong to the solution set of the inequality \( |4x-10| \leq 6 \)?
\( 4 \)
\( 2 \)
\( 3 \)
\( 0 \)
1103187404
Level:
A
The solution set of an inequality is graphed on the number line. Determine this inequality.
\( |4-x| > 41 \)
\( |x-3| < 42 \)
\( |x-2| > 42 \)
\( |1-x| > 43 \)
1003187403
Level:
C
How many solutions does the equation \( \left| |2x+6|-8\right|=4 \) have?
\( 4 \)
\( 2 \)
\( 0 \)
\( 6 \)
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?
\( \sqrt2-7+\sqrt[3]5-\pi \)
\( \sqrt{7-\pi+\sqrt[3]5+\sqrt2} \)
\( \sqrt[3]5-\pi-\sqrt2-7 \)
\( \sqrt{\pi-\sqrt[3]5-\sqrt2+7} \)