Question

{-4≤-1-5х/4≤1, х+1/3-х-2/3≥1​

Answer 1

Ответ:

1) -4 ≤ -1 - 5x/4 ≤ 1

Упростим:

-5 ≤ -5x/4 ≤ 0

Умножим на -4 и поменяем направление неравенства:

20 ≥ 5x ≥ 0

Разделим на 5:

4 ≥ x ≥ 0

2) х + 1/3 - х - 2/3 ≥ 1

1/3 - 2/3 ≥ 1

-1/3 ≥ 1

Объяснение:

Источник: ChatGPT

Answer 2

To solve the inequalities, let's take them one by one:

1. $-4 \leq -1 - \frac{5x}{4} \leq 1$

First, we'll simplify the middle part of the inequality:

$-1 - \frac{5x}{4} \leq 1$

Multiply both sides by 4 to get rid of the fraction:

$-4 - 5x \leq 4$

Now, add $5x$ to both sides:

$-4 + 5x - 5x \leq 4 + 5x$

$-4 \leq 5x$

Divide both sides by 5 (note that since 5 is positive, we don't need to change the direction of the inequality):

$-\frac{4}{5} \leq x$

So, the solution to the first inequality is $x \geq -\frac{4}{5}$.

2. $x + \frac{1}{3} - x - \frac{2}{3} \geq 1$

Simplify the left-hand side:

$\frac{1}{3} - \frac{2}{3} \geq 1$

$-\frac{1}{3} \geq 1$

This is not possible, as $-\frac{1}{3}$ is smaller than 1. Therefore, there is no solution for the second inequality.

Putting it all together:

$x \geq -\frac{4}{5}$ (from the first inequality)

There is no solution for the second inequality.

So, the solution to the system of inequalities is $x \geq -\frac{4}{5}$.