31 - 2/3X > 27, then X < ?

subtract 27 from each side, add 2/3 * x to each side.

4>2/3 * x

multiply each side by 3/2

6>x

Subtract 31 from both sides.

-(2/3)X > -4
(2/3) X < 4
X < 6

Note that the direction of > had to change to < when I multipled both sides by a negative number.

To solve 31 - 2/3X > 27, we'll isolate the variable X to find its possible values.

Step 1: Subtract 31 from both sides of the equation:
31 - 31 - 2/3X > 27 - 31
-2/3X > -4

Step 2: Multiply both sides of the equation by -3/2 (the reciprocal of -2/3). Be careful when multiplying by a negative number because it will reverse the inequality sign:
(-3/2)(-2/3X) < (-3/2)(-4)
X < (3/2)(-4)

Step 3: Simplify the right side of the equation:
X < (-12/2)
X < -6

Therefore, the solution to the inequality 31 - 2/3X > 27 is X < -6.