Please help ME!!!!!!!!!!!!!!!!!!!!!!!!!
- 2/3x < 6
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.
Multiplying both sides out we get:
+1X (or just X) = -18/2
further simplification gives us:
Thus X > -9
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:
(-2/3)x < 6 »»» (-3/2)*(-2/3)x > (6)*(-3/2)
»»» ((-3*-2)/(2*3))x > (6*-3)/(2)
»»» (6/6)x > (-18/2) »»» (1)x > (-9)
»»» x > -9
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)
x > -9
Finally, you may need to graph the solution in the number line. Can you do that? I'm sure you can!