Question

3х-13>0. 5х+3<3х-7 25-4х>0. 1-2х>х+4

Answer 1

Ответ:

1) 3х-13>0

3x>13-7

3x>6

x>6:3

x>2

Ответ: (2;+∞)

2) 5х-15>0

5x>15

x>15:5

x>3

Ответ: (3;+∞)

3) 16-4x<0

-4x<-16

x>-16:(-4)

x>4

Ответ: (4;+∞)

4) 6(х+1)>5x+3

6x+6>5x+3

6x-5x>3-6

x>-3

Ответ: (-3;+∞)

5) х-3/2>x+1/4

2(х-3)>x+1

2x-6>x+1

2x-x>1+6

x>7

Ответ: (7;+∞)

6) 2х+1/5>x-4/3

3(2x+1)>5(x-4)

6x+3>5x-20

6x-5x>-20-3

x>-23

Ответ: (-23;+∞)

Answer 2

To solve the given inequalities, let's work on each one step by step:

1. 3x - 13 > 0

To solve this inequality, we can isolate x by adding 13 to both sides of the inequality:

3x - 13 + 13 > 0 + 13 3x > 13

Now, divide both sides by 3 to solve for x:

(3x)/3 > 13/3 x > 13/3

Therefore, the solution for the first inequality is x > 13/3.

2. 5x + 3 < 3x - 7

To solve this inequality, let's isolate x on one side of the inequality. We can do this by subtracting 3x from both sides and adding 7 to both sides:

5x - 3x + 3 < 3x - 3x - 7 + 7 2x + 3 < -7

Next, subtract 3 from both sides:

2x + 3 - 3 < -7 - 3 2x < -10

Finally, divide both sides by 2:

(2x)/2 < (-10)/2 x < -5

Therefore, the solution for the second inequality is x < -5.

3. 25 - 4x > 0

To solve this inequality, we need to isolate x. Let's subtract 25 from both sides:

25 - 4x - 25 > 0 - 25 -4x > -25

Dividing both sides by -4:

(-4x)/-4 < (-25)/-4 x < 25/4

Thus, the solution for the third inequality is x < 25/4.

4. 1 - 2x > x + 4

Let's solve this inequality step by step. First, let's simplify both sides by combining like terms:

1 - 2x - x > x + 4 - x 1 - 3x > 4

Next, subtract 1 from both sides:

1 - 3x - 1 > 4 - 1 -3x > 3

To isolate x, divide both sides by -3. Note that we need to flip the inequality since we are dividing by a negative number:

(-3x)/-3 < 3/-3 x < -1

Therefore, the solution for the fourth inequality is x < -1.

To summarize:

1. x > 13/3
2. x < -5
3. x < 25/4
4. x < -1