To solve the first inequality:
3(x-2) - 5(x+3) > 27Expanding both sides:3x - 6 - 5x - 15 > 27Combining like terms:-2x - 21 > 27Adding 21 to both sides:-2x > 48Dividing by -2 (note we flip the inequality sign):x < -24
To solve the second inequality:
6x - 3(x-1) < 2 + 5xExpanding both sides:6x - 3x + 3 < 2 + 5xCombining like terms:3x + 3 < 2 + 5xSubtracting 2x from both sides:3 < 2xDividing by 2:x > 3/2
Therefore, the solutions are:x < -24x > 3/2
To solve the first inequality:
3(x-2) - 5(x+3) > 27
Expanding both sides:
3x - 6 - 5x - 15 > 27
Combining like terms:
-2x - 21 > 27
Adding 21 to both sides:
-2x > 48
Dividing by -2 (note we flip the inequality sign):
x < -24
To solve the second inequality:
6x - 3(x-1) < 2 + 5x
Expanding both sides:
6x - 3x + 3 < 2 + 5x
Combining like terms:
3x + 3 < 2 + 5x
Subtracting 2x from both sides:
3 < 2x
Dividing by 2:
x > 3/2
Therefore, the solutions are:
x < -24
x > 3/2