Question

4)6 – 5y >3y – 2 2) 3x + 1⩽ 4x – 5 5) 3 – 7y >5y - 3

Answer 1

6-5y > 3y-2

-5у-3у > -2-6

-8у > -8

у < 1

у < 1

Ответ: у∈(-∞;1)

3x+1 ≤ 4x-5

3х-4х ≤ -5-1

-х ≤ -6

х ≥ 6

Ответ: х∈[6;+∞)

3-7y > 5y-3

-7у-5у > -3-3

-12у > -6

у < 1/2

у < 0,5

Ответ: у∈(-∞;0,5)

Answer 2

To solve these inequalities, you'll want to isolate the variable (y or x) on one side of the inequality sign. Here's how you can solve each of them step by step:

1. 6 - 5y > 3y - 2

First, let's get all the terms involving y on one side and constants on the other side:

Add 5y to both sides: 6 - 5y + 5y > 3y - 2 + 5y

This simplifies to: 6 > 8y - 2

Now, add 2 to both sides to isolate 8y: 6 + 2 > 8y - 2 + 2 8 > 8y

Finally, divide both sides by 8 to solve for y: (8/8) > (8y/8) 1 > y

So, the solution to the inequality is: y < 1

2. 3x + 1 ≤ 4x - 5

First, let's get all the terms involving x on one side and constants on the other side:

Subtract 3x from both sides: 3x + 1 - 3x ≤ 4x - 5 - 3x

This simplifies to: 1 ≤ x - 5

Now, add 5 to both sides to isolate x: 1 + 5 ≤ x - 5 + 5 6 ≤ x

So, the solution to the inequality is: x ≥ 6

3. 3 - 7y > 5y - 3

First, let's get all the terms involving y on one side and constants on the other side:

Add 7y to both sides: 3 - 7y + 7y > 5y - 3 + 7y

This simplifies to: 3 > 12y - 3

Now, add 3 to both sides to isolate 12y: 3 + 3 > 12y - 3 + 3 6 > 12y

Finally, divide both sides by 12 to solve for y: (6/12) > (12y/12) 1/2 > y

So, the solution to the inequality is: y < 1/2