Question

1) 4х+12х>7+13х. 2) (2-3х)+4(6+х)>1. 3) 7-4х<6х-23. 4) (4-5х)+2(3+х)<2.

Answer 1

1)x>2,3
2)x>-25
3)x>3
4)x>2,6

Answer 2

Ответ:

1)4x+12x>7+13x

16x>7+13x

16x-13x>7

3x>7|:3

x>7/3

2)(2-3x)+4(6+x)>1

2-3x+4(6+x)>1

2-3x+24+4x>1

26-3x+4x>1

26+x>1

x>1-26

x>-25

3)7-4x<6x-23

7-4x-6x<-23

-4x-6x<-23-7

-10x<-23-7

-10x<-30|:-10

x>3

4)(4-5x)+2(3+x)<2

4-5x+2(3+x)<2

4-5x+6+2x<2

10-5x+2x<2

10-3x<2

-3x<2-10

-3x<-8|:-3

x>8/3

Answer 3

Let's solve the given inequalities step by step:

1. 4x + 12x > 7 + 13x

Combining like terms: 16x > 7 + 13x

Moving all the terms containing x to one side and the constant terms to the other side: 16x - 13x > 7

Simplifying: 3x > 7

Dividing both sides of the inequality by 3 (note: since the coefficient of x is positive, the direction of the inequality remains the same): x > 7/3

2. (2 - 3x) + 4(6 + x) > 1

Expanding the brackets: 2 - 3x + 24 + 4x > 1

Combining like terms: 26 + x > 1

Moving the constant term to the other side: x > 1 - 26

Simplifying: x > -25

3. 7 - 4x < 6x - 23

Moving all the terms containing x to one side and the constant terms to the other side: -4x - 6x < -23 - 7

Simplifying: -10x < -30

Dividing both sides of the inequality by -10 (note: since we are dividing by a negative number, the direction of the inequality flips): x > -30/-10 x > 3

4. (4 - 5x) + 2(3 + x) < 2

Expanding the brackets: 4 - 5x + 6 + 2x < 2

Combining like terms: 10 - 3x < 2

Moving the constant term to the other side: -3x < 2 - 10

Simplifying: -3x < -8

Dividing both sides of the inequality by -3 (note: since we are dividing by a negative number, the direction of the inequality flips): x > -8/-3 x > 8/3

To summarize the solutions:

1. x > 7/3
2. x > -25
3. x > 3
4. x > 8/3