1003124201 Level: BWhich equation describes real numbers \( x \) that are equidistant from the numbers \( 6 \) and \( -3 \) on the number line?\( |x-6|=|x+3| \)\( |x+6|=|x+3| \)\( |x-6|=|x-3| \)\( |x+6|=|x-3| \)
1003049203 Level: CIdentify which of the statements is false.\( \forall a\text{, }b\in\mathbb{R}\colon |a+b|=|a|+|b| \)\( \forall a\text{, }b\in\mathbb{R}\colon |a\cdot b|=|a|\cdot|b| \)\( \forall a\in\mathbb{R}\text{, }b\in\mathbb{R}\setminus\{0\}\colon|\frac ab|=\frac{|a|}{|b|} \)\( a\in\mathbb{R}\colon |a|=|-a| \)
9000081406 Level: CFor \(x\in \mathbb{R}\) find the correct relationship between \(|x|\) and \(|- x|\).\(|x| = |- x|\)\(|x| > |- x|\)\(|x| < |- x|\)None of them. The answer depends on the particular value of \(x\).
9000081407 Level: CFor \(x,y\in \mathbb{R}\) find the correct relationship between \(|x - y|\) and \(|y - x|\).\(|x - y| = |y - x|\)\(|x - y| > |y - x|\)\(|x - y| < |y - x|\)None of them. The answer depends on the particular values of \(x\), \(y\).
9000081408 Level: BFor \(x\in \mathbb{R}^{-}\) consider expressions \(|x|\), \(|- x|\), \(-|x|\) and \(- x\). Which of these attains only negative values?\(-|x|\)\(|x|\)\(|- x|\)\(- x\)
9000081409 Level: CAmong expressions \(1 + |x|\), \(|1 + x|\), \(1 -|x|\) and \(|1 - x|\) on the set \(x\in (-\infty ;-1)\) find the expression which has smaller values than the other expressions from this list.\(1 -|x|\)\(1 + |x|\)\(|1 + x|\)\(|1 - x|\)None of them.
9000078507 Level: BAssuming \(x\in \left (-\frac{1} {2};6\right )\), simplify the following expression. \[ 3 -|6 - x| + |2x + 1| \]\(3x - 2\)\(x - 2\)\(3x + 10\)\(x + 8\)
9000078506 Level: BAssuming \(x\in (-\infty ;0)\), simplify the following expression. \[ 3x -|2x|-|- x| \]\(6x\)\(4x\)\(2x\)\(0\)
9000078505 Level: BAssuming \(x\in (0;\infty )\), simplify the following expression. \[ 3x -|2x|-|- x| \]\(0\)\(2x\)\(3x\)\(4x\)