Question

A) 2 у/3-у/6<1 б) 12-2 х /3>3 х-1/4в)2z+9/5>=1-3z/7г)12-у<5(у-1)/6д)3(4 х+3)/5>4 х-3е)3z+6/5-3z-8/4 >= 2             

Answer 1

A)2y/ 3-у/6<1
  2y/3-у<6
  2y<18-6y
   8y<18
   y<2.25
  б) 12-2 х /3>3 х-1/4
48-8x>36x-3
45>44x
x>1.02

Answer 2

A) Let's solve the inequality step by step:

2y/3 - y/6 < 1

First, let's find a common denominator for the fractions, which is 6:

(2y * 2) / 6 - y / 6 < 1

(4y - y) / 6 < 1

3y / 6 < 1

Divide both sides by 3:

y / 2 < 1

Multiply both sides by 2 to eliminate the fraction:

y < 2

So the solution for the inequality is y < 2.

B) Let's solve the inequality step by step:

12 - 2x/3 > 3x - 1/4

To eliminate the fractions, let's find a common denominator, which is 12:

(12 * 12) - (2x * 4) > (3x * 12) - (1 * 12)

144 - 8x > 36x - 12

Rearrange the equation:

144 + 12 > 36x + 8x

156 > 44x

Divide both sides by 44:

156/44 > x

3.55 > x

So the solution for the inequality is x < 3.55.

C) Let's solve the inequality step by step:

2z + 9/5 >= 1 - 3z/7

To eliminate the fractions, let's find a common denominator, which is 35:

(35 * 2z + 35 * (9/5)) >= (35 * 1) - (35 * 3z/7)

70z + 63/5 >= 35 - 15z/7

Multiply both sides by 5 to eliminate the fraction:

5(70z) + 5(63/5) >= 5(35) - 5(15z/7)

350z + 63 >= 175 - 75z/7

Multiply both sides by 7 to eliminate the fraction:

7(350z) + 7(63) >= 7(175) - 7(75z/7)

2450z + 441 >= 1225 - 75z

Combine like terms:

2450z + 75z >= 1225 - 441

2525z >= 784

Divide both sides by 2525:

z >= 784/2525

So the solution for the inequality is z >= 0.310.

D) Let's solve the inequality step by step:

12 - y < 5(y - 1)/6

To eliminate the fraction, let's find a common denominator, which is 6:

(6 * 12) - 6y < 5(y - 1)

72 - 6y < 5y - 5

Add 6y to both sides:

72 < 11y - 5

Add 5 to both sides:

77 < 11y

Divide both sides by 11:

7 < y

So the solution for the inequality is y > 7.

E) Let's solve the inequality step by step:

(3(4x + 3))/5 > 4x - 3

Multiply both sides by 5 to eliminate the fraction:

5(3(4x + 3))/5 > 5(4x - 3)

3(4x + 3) > 20x - 15

Distribute on the left side:

12x + 9 > 20x - 15

Subtract 12x from both sides:

9 > 8x -