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8 > -16 12 > -12 Adding or subtracting any number to both sides of an inequality does not alter the inequality. See the proof below. -4 -4 16 > - 8 12 > -12 +4 +4 48 > -48 12 > -12 Multiplying or dividing by a positive also does not alter the direction of an inequality sign. See proof below. x4 x4 3 > - 3 12 > -12 ÷4 ÷4 -48 < 48 12 > -12 However, multiplying or dividing both sides by a negative changes the inequalitiy. See proof below. •-4 •-4 -3 < 3 12 > -12 ÷-4 ÷-4 Did the sign flip? Undo any multiplication or division with the opposite operation. Make sure you use the same sign. ÷3 ÷3 3x > 12 x > 4 Yes No Did the sign flip? Undo any multiplication or division with the opposite operation. Make sure you use the same sign. ÷-3 ÷-3 -3x > 12 x < -4 Yes No Did the sign flip? Undo any multiplication or division with the opposite operation. Make sure you use the same sign. ÷3 ÷3 3x > -12 x > - 4 Yes No Did the sign flip? Undo any multiplication or division with the opposite operation. Make sure you use the same sign. 4• x 4 x > 48 > 12 Yes No •4 Did the sign flip? Undo any multiplication or division with the opposite operation. Make sure you use the same sign. -4• -4 x x < -48 > 12 Yes No •-4 Remember multiplying or dividing both sides by a negative flips the inequality sign. -4• -4 x x < > 2 •-4 -5• -5 x x < > 2 •-5 -4 x x < > 2 x 4 x > > 5 x 12 6 x > 2 > < x 14 -7 x > -2 > < x -12 -6 x > 2 > < x 16 4 x > 4 > < x 75 5 x > 15 > < x -4 3x > -12 > < x 6 -2x > -12 > < x -6 3x > -18 > < |