My approach would be to solve for -2/3X = 6. To accomplish this you want to isolate X on one side of the equation (e.g. X=) and have a number on the other side of the equation., In this instance, in order to get X by itself on one side of the equation we need to divide both sides of the equation by -3/2 because a fraction multiplied by its own inverse (e.g. 2/1 x 1/2) equals 1. In order to keep an equation valid, whatever we do to one side of the equation we need to do to the other side as follows:

(-3/2) (-2/3) X = (6/1)(-3/2)

Note; a minus multiplied by another minus number gives you a plus value so (-2/3)(-3/2) = +1 but (6) (-3/2) gives you a negative number.

Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...

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Multiply both sides of the inequality by the reciprocal of the fractional coefficient of the variable x (i.e., multiply both sides by -3/2). Since you are multiplying by a negative number, and thus changing the signs, you must also flip the inequality symol:

Roberto C. | Highly Qualified Teacher - Algebra, Geometry and SpanishHighly Qualified Teacher - Algebra, Geom...

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If your inequality is: (-2/3)x < 6, then you just need to multiply both sides by the reciprocal of -2/3. Since you're multiplying by a negative number, you need to flip the inequality sign:

(-3/2)(-2/3)x > 6(-3/2)

Now, simplify:

x > -9

Finally, you may need to graph the solution in the number line. Can you do that? I'm sure you can!