Question

Решите неравенства: 1) 3 - 2(u - 1) > 8 + u2) 5(u + 2) + 14 < 6 - u3) 1/4 - y/3 > 1/3 - y4) 6 - 5y > 3y - 25) 3 - 7y > 5y - 36) x/6 + 1/2 > x - 1/3​

Answer 1

Ответ:

1) u< -1

2) u  <  - 3

3)  y > 1/8

4) y > 1

5) y< 1/2

6) х < 1

Пошаговое объяснение:

1) 3 - 2(u - 1) > 8 + u

3 - 2u + 2 > 8 + u

5- 2u  > 8 + u

-2u - u > 8-5

-3u > 3

u< -1

u ∈ ( -∞, -1)

2) 5(u + 2) + 14 < 6 - u

5u + 10 + 14 < 6 - u

5u + 24 < 6 - u

5u + u < 6 - 24

6u < -18

u  <  - 3

u ∈ ( -∞, -3)

3) 1/4 - y/3 > 1/3 - y

3 - 4y > 4 - 12y

-4y + 12y > 4 - 3

8y > 1

y > 1/8

y ∈ (1/8, +∞ )

4) 6 - 5y > 3y - 2

-5y - 3y >  - 2 - 6

-8y > -8

y > 1

y ∈ ( -∞, -1)

5) 3 - 7y > 5y - 3

-7y - 5y >- 3-3

-12y> -6

y< 1/2

y ∈ ( -∞, 1/2)

6)x/6 + 1/2 > x - 1/3​

x + 3 > 6х -2

x- 6х > -2-3

-5х > -5

х < 1

х ∈ ( -∞, 1)

Answer 2

Let's solve these inequalities step by step:

1. $3 - 2(u - 1) > 8 + u$

First, distribute the -2 on the left side:

$3 - 2u + 2 > 8 + u$

Combine like terms:

$-2u + 5 > 8 + u$

Subtract u from both sides:

$-3u + 5 > 8$

Subtract 5 from both sides:

$-3u > 3$

Divide by -3 (remembering to reverse the inequality sign when dividing by a negative number):

$u < -1$

2. $5(u + 2) + 14 < 6 - u$

First, distribute the 5 on the left side:

$5u + 10 + 14 < 6 - u$

Combine like terms:

$5u + 24 < 6 - u$

Add u to both sides:

$6u + 24 < 6$

Subtract 24 from both sides:

$6u < -18$

Divide by 6:

$u < -3$

3. $\frac{1}{4} - \frac{y}{3} > \frac{1}{3} - y$

First, let's get rid of the fractions by multiplying through by 12 (the least common denominator):

$3(1) - 4y > 4 - 12y$

Simplify:

$3 - 4y > 4 - 12y$

Add 12y to both sides:

$12y + 3 > 4$

Subtract 3 from both sides:

$12y > 1$

Divide by 12:

$y > \frac{1}{12}$

4. $6 - 5y > 3y - 2$

Add 5y to both sides:

$6 > 8y - 2$

Add 2 to both sides:

$8 > 8y$

Divide by 8:

$y < 1$

5. $3 - 7y > 5y - 3$

Add 7y to both sides:

$3 > 12y - 3$

Add 3 to both sides:

$6 > 12y$

Divide by 12:

$y < \frac{1}{2}$

6. $\frac{x}{6} + \frac{1}{2} > x - \frac{1}{3}$

First, let's get rid of the fractions by multiplying through by 6:

$x + 3 > 6x - 2$

Subtract x from both sides:

$3 > 5x - 2$

Add 2 to both sides:

$5 > 5x$

Divide by 5:

$x < 1$

So, the solutions are:

1. $u < -1$

2. $u < -3$

3. $y > \frac{1}{12}$

4. $y < 1$

5. $y < \frac{1}{2}$

6. $x < 1$