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.