x2 + 2x - 8 ≤ 0
( x + 4 )( x - 2 ) ≤ 0
Since ( x + 4 )( x - 2 ) ≤ 0, either ( x + 4 ) ≥ 0 AND ( x - 2 ) ≤ 0 OR ( x + 4 ) ≤ 0 AND ( x - 2 ) ≥ 0
( + )( - ) ≤ 0 OR ( - )( + ) ≤ 0
[ x + 4 ≥ 0 AND x - 2 ≤ 0 ] OR [ x + 4 ≤ 0 AND x - 2 ≥ 0 ] can be simplified to:
[ x ≥ -4 AND x ≤ 2 ] OR [ x ≤ -4 AND x ≥ 2 ]
[ x ≥ -4 AND x ≤ 2 ] can be re-written as [ -4 ≤ x AND x ≤ 2 ], then simplified to [ -4 ≤ x ≤ 2 ].
[ x ≤ -4 AND x ≥ 2 ] results in the empty set (Φ), since there are no numbers that are both less than or equal to -4 AND greater than or equal to 2
[ x ≥ -4 AND x ≤ 2 ] OR [ x ≤ -4 AND x ≥ 2 ] = [ -4 ≤ x ≤ 2 ] OR Φ
[ -4 ≤ x ≤ 2 ] OR Φ = -4 ≤ x ≤ 2