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Pan African
2013 Pan African
3
Solve the system of inequalities
Solve the system of inequalities
Source: Pan African MO 2013 Q6
June 30, 2013
inequalities
inequalities unsolved
Problem Statement
Let
x
x
x
,
y
y
y
, and
z
z
z
be real numbers such that
x
<
y
<
z
<
6
x<y<z<6
x
<
y
<
z
<
6
. Solve the system of inequalities:
{
1
y
−
x
+
1
z
−
y
≤
2
1
6
−
z
+
2
≤
x
\left\{\begin{array}{cc} \dfrac{1}{y-x}+\dfrac{1}{z-y}\le 2 \\ \dfrac{1}{6-z}+2\le x \\ \end{array}\right.
⎩
⎨
⎧
y
−
x
1
+
z
−
y
1
≤
2
6
−
z
1
+
2
≤
x
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