x2−2x−8≤−x+2
x2−2x−8≤−x+2 ,x∈[∞,−2]∪[4,+∞]
Separate into possible cases
x2−2x−8≤−x+2,−x+2≥0
x2−2x−8≤−x+2,−x+2<0
Solve for inequality x
x≤6,−x+2≥0
x2−2x−8≤−x+2,−x+2<0
x≤6,x≤2
x2−2x−8≤−x+2,−x+2<0
Since the left hand side is always positive or Zero and the right hand is always negative the statement is false for any value of x
x≤6,x≤2
x∈∅,−1+2<0
x∈∅,1>2
Find the intersection
x∈[−∞,−2]
x∈∅
Find the union
x∈[−∞,2],x∈[−∞,−2]∪[4,+∞]
Find the intersection of the solution and the defined range
x∈[−∞,−2]
Alternate form
x≤−2
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