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If x > y and y > z, which of the following represents the greatest number?

Explanation	Calculations	Help
$We first note the given inequalities.$	$x > y y > z$
$We apply "Chain Rule for Inequalities" to combine them.$	$x > z$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We subtract y from both sides of x > y to find the sign of x - y .$	$x - y > 0$
$We subtract z from both sides of x > z to find the sign of x - z .$	$x - z > 0$
$We express x - z as the sum of the positive differences x - y and y - z .$	$x - z = (x - y) + (y - z)$	Theory & Tactics Method Card CALC2-A Click to view full details
$Since both x - y and y - z are positive, their sum x - z is the greatest among the listed expressions.$

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x - z

If x > y and y > z, which of the following represents the greatest number?

Explanation	Calculations	Help
$We first note the given inequalities.$	$x > y y > z$
$We apply "Chain Rule for Inequalities" to combine them.$	$x > z$	Theory & Tactics Method Card INEQ1-C Click to view full details
$We subtract y from both sides of x > y to find the sign of x - y .$	$x - y > 0$
$We subtract z from both sides of x > z to find the sign of x - z .$	$x - z > 0$
$We express x - z as the sum of the positive differences x - y and y - z .$	$x - z = (x - y) + (y - z)$	Theory & Tactics Method Card CALC2-A Click to view full details
$Since both x - y and y - z are positive, their sum x - z is the greatest among the listed expressions.$

Scroll horizontally to view all columns

x - z