Question

Решите неравенство:1)9-5х+1/2>2 2)1,75+2х/3<+12/3 3)4+у/2-у+2/7<у+3 4)4+7у-3/5>3у+5/4-3у/2

Answer 1

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Answer 2

1. 9 - 5x + 1/2 > 2

To solve this inequality, we need to isolate the variable x on one side of the inequality sign. Let's begin by subtracting 9 from both sides:

9 - 5x + 1/2 - 9 > 2 - 9

Simplifying the left side, we get:

-5x + 1/2 > -7

Next, let's subtract 1/2 from both sides:

-5x + 1/2 - 1/2 > -7 - 1/2

Simplifying the left side, we get:

-5x > -7.5

Finally, we can isolate x by dividing both sides by -5 (and reversing the inequality sign since we are dividing by a negative number):

x < 3/2

Therefore, the solution to the inequality is x < 3/2.

2. 1.75 + 2x/3 <= 4

To solve this inequality, we need to isolate the variable x on one side of the inequality sign. Let's begin by subtracting 1.75 from both sides:

1.75 + 2x/3 - 1.75 <= 4 - 1.75

Simplifying the left side, we get:

2x/3 <= 2.25

Next, let's multiply both sides by 3/2:

(2x/3) * (3/2) <= 2.25 * (3/2)

Simplifying both sides, we get:

x <= 3.375

Therefore, the solution to the inequality is x <= 3.375.

3. 4 + y/2 - y + 2/7 < y + 3

To solve this inequality, we need to isolate the variable y on one side of the inequality sign. Let's begin by subtracting 4 from both sides:

4 + y/2 - y + 2/7 - 4 < y + 3 - 4

Simplifying both sides, we get:

y/2 - y + 2/7 < y - 1

Next, let's add y to both sides:

y/2 - y + 2/7 + y < y - 1 + y

Simplifying both sides, we get:

y/2 + 2/7 < 2y - 1

Next, let's subtract 2/7 from both sides:

y/2 + 2/7 - 2/7 < 2y - 1 - 2/7

Simplifying both sides, we get:

y/2 < 2y - 15/7

Finally, let's subtract y/2 from both sides:

y/2 - y/2 < 2y - y/2 - 15/7

Simplifying both sides, we get:

0 < 3/2 y - 15/7

Next, let's add 15/7 to both sides:

15/7 < 3/2 y

Finally, let's divide both sides by 3/2:

10/7 < y

Therefore, the solution to the inequality is y > 10/7.

4. 4 + 7y - 3/5 > 3y + 5/4 - 3y/2

To solve this inequality, we need to simplify both sides as much as possible. Let's begin by simplifying the right side:

4 + 7y - 3/5 > 5/4 - 3y/2

Next, let's add