2 + 6x > -8 + 30
Combine like terms
6x > 22
Divide both sides by 6
x > 22/6
x > 11/3

5x + 6x > 2(3x - 1)
Combine like terms
11x > 6x - 2
Subtract 6x from both sides
5x > -2
Divide both sides by 5
x > -2/5

5x^2 - 8x + 3 < 0
Factor the quadratic expression
(5x - 3)(x - 1) < 0
Determine the critical points where the expression is equal to 0
5x - 3 = 0
x = 3/5
x - 1 = 0
x = 1
The critical points divide the number line into three intervals: (-∞, 3/5), (3/5, 1), and (1, ∞)
Test a value in each interval to determine where the expression is less than 0
When x = 0, (5(0)^2 - 8(0) + 3) = 3 > 0
When x = 1/2, (5(1/2)^2 - 8(1/2) + 3) = 3/4 < 0
When x = 2, (5(2)^2 - 8(2) + 3) = 5 > 0
Therefore, the solution is 3/5 < x < 1

x^2 - 3x - 4 > 0
Factor the quadratic expression
(x - 4)(x + 1) > 0
Determine the critical points where the expression is equal to 0
x - 4 = 0
x = 4
x + 1 = 0
x = -1
The critical points divide the number line into three intervals: (-∞, -1), (-1, 4), and (4, ∞)
Test a value in each interval to determine where the expression is greater than 0
When x = -2, ((-2)^2 - 3(-2) - 4) = 6 > 0
When x = 0, ((0)^2 - 3(0) - 4) = -4 < 0
When x = 5, ((5)^2 - 3(5) - 4) = 6 > 0
Therefore, the solution is x < -1 or x > 4