Question

1034. 1) 3x + (5x – 2) < 3 – 2 x ,[4(5x – 1) – 21 x > 1 – 3 x;2)17 - 11x < 9 x – 2(5x + 7),6 – x > 2(1 – 4 x) – 3(1 – 3 x ).​

Answer 1

Ответ:

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Answer 2

Let's solve each of the inequalities step by step:

1. 3x + (5x – 2) < 3 – 2x

First, simplify both sides of the inequality:

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

Combine like terms:

8x - 2 < 3 - 2x

Now, let's isolate the x terms on one side and the constants on the other:

8x + 2x < 3 + 2

10x < 5

Now, divide both sides by 10:

x < 5/10

Simplify:

x < 1/2

So the solution to the first inequality is:

x < 1/2

2. 4(5x – 1) – 21x > 1 – 3x

First, distribute the 4 on the left side:

20x - 4 - 21x > 1 - 3x

Combine like terms:

-1x - 4 > 1 - 3x

Now, let's isolate the x terms on one side and the constants on the other:

-1x + 3x > 1 + 4

2x > 5

Now, divide both sides by 2:

x > 5/2

So the solution to the second inequality is:

x > 5/2

3. 17 - 11x < 9x – 2(5x + 7)

First, distribute the -2 on the right side:

17 - 11x < 9x - 10x - 14

Combine like terms:

17 - 11x < -x - 14

Now, let's isolate the x terms on one side and the constants on the other:

-11x + x < -14 - 17

-10x < -31

Now, divide both sides by -10 (remember to reverse the inequality when dividing by a negative number):

x > 31/10

So the solution to the third inequality is:

x > 31/10

4. 6 – x > 2(1 – 4x) – 3(1 – 3x)

First, simplify both sides of the inequality:

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

Combine like terms:

6 - x > -1 + x

Now, let's isolate the x terms on one side and the constants on the other:

6 + 1 > x + x

7 > 2x

Now, divide both sides by 2:

7/2 > x

So the solution to the fourth inequality is:

x < 7/2

To summarize the solutions:

1. x < 1/2
2. x > 5/2
3. x > 31/10
4. x < 7/2