Question

1,5х(3+2х)=3х(х+1)-30 решить неравенство

Answer 1

1,5х(3+2х)=3х(х+1)-30

$\frac{3}{2} x$(3+2х)=3х(х+1)-30 | *2

3x(3+2х)=6х(х+1)-60 | :3

x(3+2х)=2х(х+1)-20

x(3+2х)-2х(х+1)+20=0

(3+2x-2(x+1))x+20=0

(3+2x-2x-2)x+20=0

x+20=0

x=-20

Answer 2

3/2x(3+2x)=3x(x+1)-30

3x(3+2x)=6x(x+1)-60

x(3+2x)=2x(x+1)-20

x(3+2x)-2x(x+1)+20=0

(3+2x-2(x+1))x+20=0

(3+2x-2x-2)x+20=0

x+20=0

x=-20

Answer 3

To solve the inequality, we'll first simplify the expressions on both sides of the inequality and then isolate the variable x. Here's the step-by-step solution:

1. Simplify the expressions on both sides: 1.5x(3 + 2x) = 3x(x + 1) - 30

2. Expand and combine like terms: 4.5x + 3x^2 = 3x^2 + 3x - 30

3. Move all terms to one side of the equation: 3x^2 + 3x - 30 - 4.5x = 0

4. Combine like terms: 3x^2 - 1.5x - 30 = 0

5. Now we need to solve the quadratic equation. We can either factor it or use the quadratic formula. Let's use the quadratic formula: The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / 2a

   For our equation: a = 3, b = -1.5, and c = -30

   x = [1.5 ± √((-1.5)^2 - 4 * 3 * (-30))] / 2 * 3

   x = [1.5 ± √(2.25 + 360)] / 6

   x = [1.5 ± √362.25] / 6

   x = [1.5 ± 19.05] / 6

6. Now, we have two possible solutions: a) x = (1.5 + 19.05) / 6 = 3.25 b) x = (1.5 - 19.05) / 6 = -2.84 (rounded to two decimal places)

7. So, the solutions to the inequality are: x ≥ 3.25 x ≤ -2.84