Question

1) 5x>2-12x+4 ------------- 6-15x 2)7x>2-x --------- 2-13x-7x>2 3)2x>2+2x-24 ------------ (6-2x)>2 4)1-6c+y-6cy ------------ 1-112c-36c

Answer 1

3х^2 - 5x - 24 = x^2 - 12x + 36
3x^2 - x^2 - 5x + 12x - 24 - 36 = 0
2x^2 + 7x - 60 = 0
D = 49 - 4*(-60)*2 = 49 + 480 = 529     √D = 23
x1 = (-7 + 23)/4 = 4
x2 = (-7 - 23)/4 = -7,5
Ответ: х1 = 4;   х2 = - 7,5

Answer 2

Let's solve each of the given inequalities step by step:

1. 5x > 2 - 12x + 4

To solve this inequality, we'll combine like terms and isolate the variable x on one side:

5x + 12x > 2 + 4

17x > 6

Divide both sides of the inequality by 17 (since x is being multiplied by 17):

x > 6/17

Therefore, the solution to this inequality is x > 6/17.

2. 7x > 2 - x

To solve this inequality, we'll combine like terms and isolate the variable x on one side:

7x + x > 2

8x > 2

Divide both sides of the inequality by 8:

x > 2/8

Simplifying the fraction:

x > 1/4

Therefore, the solution to this inequality is x > 1/4.

Next, we have 2 - 13x - 7x > 2. Simplifying this inequality:

2 - 20x > 2

Subtracting 2 from both sides of the inequality:

-20x > 0

Dividing both sides of the inequality by -20 (remembering to flip the direction of the inequality since we're dividing by a negative number):

x < 0

Therefore, the solution to this inequality is x < 0.

3. 2x > 2 + 2x - 24

To solve this inequality, we'll combine like terms and isolate the variable x on one side:

2x - 2x > 2 - 24

0x > -22

0 > -22

Since 0 is not greater than -22, this inequality has no solution.

4. 1 - 6c + y - 6cy > 1 - 112c - 36c

To solve this inequality, we'll combine like terms and isolate the variables on one side:

-6c + 6cy + 112c + 36c > 1 - 1 + y

146c + 6cy > y

Therefore, the solution to this inequality is y < 146c + 6cy.