Question

2.3.3x + 3 < 2x+13x - 2 >4x + 2​

Answer 1

Ответ:

Смотри решение на фото

Answer 2

To solve the inequality $2.3 \cdot 3x + 3 < 2x + 13x - 2 > 4x + 2$, we can simplify it step by step.

Let's break it down:

1. $2.3 \cdot 3x + 3 < 2x + 13x - 2$

First, simplify the left side:

$6.9x + 3 < 2x + 13x - 2$

2. Now, combine like terms on both sides of the inequality:

$6.9x + 3 < 15x - 2$

3. Next, move all the $x$ terms to one side by subtracting $6.9x$ from both sides:

$3 < 8.1x - 2$

4. Add 2 to both sides:

$3 + 2 < 8.1x$

$5 < 8.1x$

5. Finally, divide both sides by 8.1 to isolate $x$:

$\frac{5}{8.1} < x$

Now, let's simplify this further:

$\frac{5}{8.1} < x \approx 0.617$

So, the solution to the inequality is $x$ is greater than approximately 0.617.

Now, let's work on the second part of the inequality:

$2x + 13x - 2 > 4x + 2$

1. Combine like terms on both sides:

$15x - 2 > 4x + 2$

2. Move all the $x$ terms to one side by subtracting $4x$ from both sides:

$15x - 4x - 2 > 2$

3. Combine like terms:

$11x - 2 > 2$

4. Add 2 to both sides:

$11x - 2 + 2 > 2 + 2$

$11x > 4$

5. Finally, divide both sides by 11 to isolate $x$:

$\frac{11x}{11} > \frac{4}{11}$

$x > \frac{4}{11}$

So, the solution to the second part of the inequality is $x$ is greater than $\frac{4}{11}$.

Therefore, the overall solution to the inequality $2.3 \cdot 3x + 3 < 2x + 13x - 2 > 4x + 2$ is:

$\frac{4}{11} < x < 0.617$