3(5x-4) > 4 (3x-2)?

15x - 12 > 12x - 8
3x > 4
x > 4 / 3

1. Distribute the 3 and 4 to the following perenthesis and get 15x-12>12x-8

2. Bring one term from each side to the other side of the inequality so that you can combine like terms, leaving you with 3x>4

3. then you have to solve by isolating the variable by dividing each side of the inequality by 3

4. Giving you your answer: x>4/3

note: treat inequality signs as equality sign first before solving)

3(5x-4) > 4 (3x-2) simplify
15x - 12 > 12x - 8 put all variables in one side adn all constants to the other side.

15x - 12x > -8 + 12
3x > 4 divide both side of the equaiton by 3
x > 4/3

15x - 12 > 12x -8
15x -12x > -8 +12
3x > 4
x > 4/3

2/5x + (3x - 4)/2x > (x - 2)/3x, (x ≠ 0) 2/5x + (3x - 4)/2x − (x - 2)/3x > 0 12/30x + 15(3x - 4)/30x − 10(x - 2)/30x > 0 [12 + 15(3x - 4) - 10(x - 2)]/30x > 0 (12 + 45x - 60 - 10x + 20)/30x > 0 (35x - 28)/30x > 0 (7/30)(5x - 4)/x > 0 Dividing each side by the positive 7/30: (5x - 4)/x > 0 For x ≠ 0, (5x - 4)/x has the same sign as the quadratic polynomial (5x - 4) x. Therefore (5x - 4) x > 0 x must be outside the interval [0,4/5] x ∈ (-∞,0) ∪ (4/5,∞)

3(5x - 4) > 4(3x - 2)
15x - 12 > 12x - 8
15x - 12x > 12 - 8
3x > 4
x > 4/3
x > 1 1/3

what makes 3(5x-4) bigger than 4(3x-2)?

3(5x-4) = 4(3x-2) , lets solve

15x-12 = 12x - 8

15x - 12x = -8+12

3x = 4

x= 4/3=1,33

lets test this inequality

3(5*1,33-4) = 7,95 (x=1,33)
3(5*2-4) = 18 (x=2)

4(3*1,33-2) = 7,96 (x=1,33)
4(3*2-2) = 16 (x=2)

we see that when x > 1,33 then 3(5x-4) is bigger than 4(3x-2) so the answer is

answer: x > 1,33

15x - 12 > 12x - 8

15x -12x > 12 - 8

3x > 4

x > 4/3

3(5x-4) > 4 (3x-2)

3(5x-4)
= 15x-12
15x=12
x = 12/15
x = 12/15 * 3/3
x= 4/5
x= 0.8


4 (3x-2)
=12x-8
12x=8
x=8/12
x=2/3
x= 0.67

0.8 > 0.67

yes it is true that 3(5x-4) is greater than 4(3x-2)