Solve -2(3x+2y-3)>12

- 2 ( 3 x + 2 y - 3 ) > 12

- 2 * 3 x - 2 * 2 y - 2 * ( - 3 ) > 12

- 6 x - 4 y + 6 > 12

- 4 y > 12 + 6 x - 6

- 4 y > 6 x + 6

- 4 y > 6 ( x + 1 ) Divide both sides by - 4

If you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality sign!

y < - 6 ( x + 1 ) / 4

y < -3 ( x + 1 ) / 2

y < 3 x / 2 - 3 / 2

remark:

y < - 6 ( x + 1 ) / 4

are same as

y < 6 ( x + 1 ) / - 4

To solve the inequality -2(3x + 2y - 3) > 12, we will follow these steps:

Step 1: Distribute the -2 to each term inside the parentheses:
-6x - 4y + 6 > 12

Step 2: Rearrange the terms so that the inequality sign is on the right side:
-6x - 4y > 12 - 6

Step 3: Simplify the right side of the inequality:
-6x - 4y > 6

Step 4: Divide the entire inequality by -2, remembering to flip the direction of the inequality sign because we are dividing by a negative number. This step is important because we want to isolate the variable terms:
(-6x - 4y)/-2 < 6/-2

Simplifying, we have:
3x + 2y < -3

So, the solution to the inequality -2(3x + 2y - 3) > 12 is 3x + 2y < -3.