Question

Решите неравенство 1)3x+1≤4x-5; 2)6-5y>3y-2; 3)x/6+1/2>x-1/3;

Answer 1

3x+1 ≤4x-5
3x-4x ≤-5-1
-1x ≤-6
знак в другую сторону
x больше 6

6-5y>3y-2
6+2>3y+5y
8>8y
x>9

Answer 2

1. 3x + 1 ≤ 4x - 5

We can simplify this inequality by subtracting 3x from both sides:

1 ≤ x - 5

Then we can add 5 to both sides:

6 ≤ x

Therefore, the solution to the inequality is x ≥ 6.

2. 6 - 5y > 3y - 2

We can simplify this inequality by adding 5y to both sides:

6 > 8y - 2

Then we can add 2 to both sides:

8 > 8y

Finally, we can divide both sides by 8:

1 > y

Therefore, the solution to the inequality is y < 1.

3. x/6 + 1/2 > x - 1/3

We can simplify this inequality by subtracting x/6 from both sides:

1/2 > 5x/6 - 1/3

Then we can add 1/3 to both sides:

5/6 > 5x/6

Finally, we can divide both sides by 5/6:

1 > x

Therefore, the solution to the inequality is x < 1.