Question

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

Answer 1

1. 7-11x <9x-10x-14

7-11x <-x-14

-11x+x>-14-7

-10x>-21

x <-21:(-10)

x <2,1

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

6-x>x-1

-x-x>-1-6

-2x>-7

x <-7:(-2)

x<3,5

Answer 2

Let's solve the given inequalities step by step:

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

   Distributing the negative sign inside the parentheses: 7 - 11x < 9x - 10x - 14

   Combining like terms: 7 - 11x < -x - 14

   Adding 11x to both sides to isolate the variable: 7 < -x - 14 + 11x

   Simplifying further: 7 < -14 + 10x

   Adding 14 to both sides: 21 < 10x

   Dividing both sides by 10 (remember to reverse the inequality when dividing by a negative number): 21/10 > x

   Therefore, the solution is x < 21/10.

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

   Distributing the numbers inside the parentheses: 6 - x > 2 - 8x - 3 + 9x

   Combining like terms: 6 - x > -1 + x

   Subtracting x from both sides to isolate the variable: 6 - x - x > -1 + x - x

   Simplifying further: 6 - 2x > -1

   Adding 2x to both sides: 6 > -1 + 2x

   Subtracting 2 from both sides: 7 > 2x

   Dividing both sides by 2: 7/2 > x

   Therefore, the solution is x < 7/2.

To summarize:

1. x < 21/10
2. x < 7/2