Question

4(x + 1) < 3(x – 3) – x,{4(2 x - 1)<3(3 x - 2).​

Answer 1

Ответ:

Пошаговое объяснение:

4(x + 1) < 3(x – 3) – x,

{

4(2 x - 1)<3(3 x - 2)

4х+4< 3x-9-x

8x-4<9x-6

4x-2x< -9-4

8x-9x< -6+4

2x < -13

- x < -2

x  < - 6,5

x > 2

x є (пустое множество)

Answer 2

To solve the inequalities, we'll start by simplifying and isolating the variable on one side of the inequality sign. Let's solve each inequality step by step:

1. 4(x + 1) < 3(x - 3) - x

Step 1: Distribute on both sides of the inequality. 4x + 4 < 3x - 9 - x

Step 2: Combine like terms on the right side of the inequality. 4x + 4 < 2x - 9

Step 3: Move all the x terms to the left side and the constants to the right side. 4x - 2x < -9 - 4

Step 4: Simplify the left side. 2x < -13

Step 5: Divide by 2 (positive value) to isolate x. x < -13 / 2

So the solution to the inequality is x < -6.5.

2. {4(2x - 1) < 3(3x - 2)

Step 1: Distribute on both sides of the inequality. 8x - 4 < 9x - 6

Step 2: Move all the x terms to the left side and the constants to the right side. 8x - 9x < -6 + 4

Step 3: Simplify the left side. -x < -2

Step 4: Divide by -1 (negative value, so the inequality sign flips) to isolate x. x > 2

So the solution to the second inequality is x > 2.

To summarize:

1. The solution to 4(x + 1) < 3(x - 3) - x is x < -6.5.
2. The solution to 4(2x - 1) < 3(3x - 2) is x > 2.