Question

7 - 11x < 9x - 2(5x + 7),6 - x > 2(1 - 4x) - 3(1 – 3x).​

Answer 1

Ответ:

1) 7-11х<9х-10х-17

-11х-9х+10х<-14-7

-10х<-21 |:(-10)

х>2,1

Ответ (2.1; +∞)

2) 6-х>2-8х-3+9х

-х+8х-9х>2-3-6

-2х>-7 |:(-2)

х<3,5

Ответ: (-∞; 3,5)

Answer 2

Let's solve each inequality step by step:

1. 7 - 11x < 9x - 2(5x + 7):

Start by simplifying the equation:

7 - 11x < 9x - 10x - 14

Combine like terms:

7 - 11x < -x - 14

Add 11x to both sides to isolate the variable:

7 < -x - 14 + 11x

7 < 12x - 14

Add 14 to both sides:

21 < 12x

Divide by 12 (since the coefficient of x is 12):

21/12 < x

Simplify:

7/4 < x

So the solution to the first inequality is x > 7/4 or x > 1.75.

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

Start by simplifying the equation:

6 - x > 2 - 8x - 3 + 9x

Combine like terms:

6 - x > -1 + x

Add x to both sides to isolate the variable:

6 > -1 + 2x

Add 1 to both sides:

7 > 2x

Divide by 2:

7/2 > x

So the solution to the second inequality is x < 7/2 or x < 3.5.

To summarize:

1. x > 7/4 or x > 1.75
2. x < 7/2 or x < 3.5