Question

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

Answer 1

Ответ:

{

4(5x−1)−21x≥1−3x

3x+(5x−2)≤3−2x

{

20x−4−21x≥1−3x

8x−2≤3−2x

{

2x≥5

10x≤5

{

x≥2.5

x≤0.5

очевидно, что нет решений.

\left \{ {{7-11x \textless 9x -2(5x+7)} \atop {6-x \textgreater 2(1-4x) - 3(1-3x)}} \right. \left \{ {{7-11x \textless 9x -10x -14} \atop {6-x \textgreater2 - 8x - 3+9x)}} \right. \left \{ {{21 \textless 10x} \atop {7 \textgreater 2x)}} \right. \left \{ {{2.1 \textless x} \atop {3.5\textgreater x)}} \right. \Leftrightarrow x \in (2.1; 3.5){

6−x\textgreater2(1−4x)−3(1−3x)

7−11x\textless9x−2(5x+7)

{

6−x\textgreater2−8x−3+9x)

7−11x\textless9x−10x−14

{

7\textgreater2x)

21\textless10x

{

3.5\textgreaterx)

2.1\textlessx

⇔x∈(2.1;3.5)

Answer 2

To solve these inequalities, you can follow the same basic principles as you would with equations. The main difference is that when you multiply or divide by a negative number, you need to reverse the inequality sign. Here are the solutions for each of your inequalities:

1. 3x + (5x - 2) < 3 - 2x

First, simplify the expression:

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

Combine like terms:

8x - 2 < 3 - 2x

Add 2x to both sides to get the x terms on one side:

10x - 2 < 3

Add 2 to both sides:

10x < 5

Now, divide both sides by 10:

x < 5/10

Simplify:

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:

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

-x - 4 > 1 - 3x

Add 3x to both sides to get the x terms on one side:

2x - 4 > 1

Add 4 to both sides:

2x > 5

Now, divide both sides by 2:

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

Add 11x to both sides to get the x terms on one side:

17 < 10x - 14

Add 14 to both sides:

31 < 10x

Now, divide both sides by 10:

31/10 < x

4. 6 - x > 2(1 - 4x) - 3(1 - 3x)

First, distribute on both sides:

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

Combine like terms:

6 - x > -1 + x

Add x to both sides to get the x terms on one side:

6 > -1 + 2x

Add 1 to both sides:

7 > 2x

Now, divide both sides by 2:

7/2 > x

So, the solutions to the given inequalities are as follows:

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