Solve the inequality √(x2-2x-8) ≤ -x+2
"\\sqrt{x^2-2x-8} \u2264 -x+2"
"\\sqrt{x^2-2x-8} \u2264 -x+2" ",x\u2208[\u221e,\u2212 2]\u222a[4,+\u221e]"
Separate into possible cases
"\\sqrt{x^2-2x-8} \u2264 -x+2, -x+2\u22650"
"\\sqrt{x^2-2x-8} \u2264 -x+2, -x+2<0"
Solve for inequality x
"x\u22646,-x+2\u22650"
"\\sqrt{x^2-2x-8} \u2264 -x+2, -x+2<0"
"x\u22646,x\u22642"
"\\sqrt{x^2-2x-8} \u2264 -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\u22646,x\u22642"
"x\\in\\varnothing,-1+2<0"
"x\\in\\varnothing,1>2"
Find the intersection
"x\\in [-\u221e,-2]"
"x\\in\\varnothing"
Find the union
"x\u2208[-\u221e,2],x\u2208[-\u221e,\u2212 2]\u222a[4,+\u221e]"
Find the intersection of the solution and the defined range
"x\\in [-\u221e,-2]"
Alternate form
"x\u2264-2"
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